The signal, (a) x(t) = 3cos(4t) is periodic with period T = pi/2. To see this, we can compute:
x (t + T) = 3cos (4(t + pi/2)) = 3cos (4t + 2pi) = 3cos(4t)
which shows that the signal repeats itself every T = pi/2 seconds.
[tex](b) \times (t) = e^{( - t)} [/tex]
This signal is not periodic.
[tex]e^{(-t)} = e^{(-(t+T))} [/tex]
for all t.
However, this is not possible since e^(-t) approaches 0 as t approaches infinity. Therefore, the signal is not periodic.
[tex](c) \times (t) = [cos (2t - \frac{\pi}{3}] ^2[/tex]
This signal is periodic with period T = pi. To see this, we can compute:
[tex]x (t + T) = [cos (2(t + \pi) - \pi/3)] ^2 = [cos (2t + 5\pi/3)] ^2 = [cos (2t - pi/3)] ^2 = x(t) \\
(d) x(t) = cos(4t) u(t) + sin(4t) u(-t)[/tex]
This signal is not periodic. To see this, suppose that there exists a period T such that x(t) = x (t + T) for all t. Then we must have:
cos(4t) u(t) + sin(4t) u(-t) = cos(4(t+T)) u(t+T) + sin(4(t+T)) u(-(t+T)) for all t.
However, this is not possible since the two terms on the left-hand side have different signs for t < 0, whereas the two terms on the right-hand side have the same sign for t < -T.
Therefore, the signal is not periodic.
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The goal of an experimental research study is which of the following? A. To make an observation to determine the correlation between two variables B. To make an observation without manipulating any variables C. To demonstrate the existence of a cause-and-effect relationship between two variables D. To make an observation to determine the relationship among several variables
Option c is correct- To demonstrate the existence of a cause-and-effect relationship between two variables.
The goal of experimental research study is different from the goal of non experimental research. The experiment attempts to show the change in one variable due to change in another variable.
The goal of the experimental method is to provide more definitive conclusions about the causal relationships among the variables in a research hypothesis than what is available from correlational research.
To accomplish this goal the an experiment control extraneous variables and manipulate independent variables. The experiment is done by changing one variable by manipulating which causes change in another variable. The researcher must control the research situation.
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4. Relaciona y encierra la respuesta correcta.
a) al, b2, c3, d4
b) a4, b3, c3, d1
c) a2, b3, c1, d4
d) a4, b1, c3, d2
Answer:
[tex]\boxed{\begin{minipage}{7cm}\\b) a4, b3, c3, d1 is the correct answer. why? B is only missing 50 percent and c only has 10 percent and finally only missing 20 percent a d\end{minipage}}\\\\\\\boxed{\begin{minipage}{7cm}\\Therfore, the correct answer is b) a4, b3, c3, d1. \end{minipage}}[/tex]
Which is the better deal?(Proportional Reasoning)
Deal A: % gallons of gas for %15.70 or Deal B. 11 gallons of gas for $42.00.Explain and Show work
Deal A is better if the cost of one gallon of gas under Deal A is less than $3.82.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Deal A offers % off the price of the gas. Let's say the regular price per gallon is $x. Then, the discounted price per gallon would be:
x - 0.5x = 0.5x
So, the cost of one gallon of gas under Deal A would be 0.5x.
We don't know the regular price per gallon, but we do know that the cost of % gallons under Deal A is $15.70. So, we can set up the following proportion:
% / 1 = $15.70 / 0.5x
% = 15.7 / 0.5x
Deal B offers 11 gallons of gas for $42.00. So, the cost of one gallon of gas under Deal B would be:
$42.00 / 11 = $3.82 (rounded to two decimal places)
Therefore, Deal A is better if the cost of one gallon of gas under Deal A is less than $3.82.
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in the form, y=a(1+r)^t PLEASEEEEEE
Answer:
y
a= ——
(r + 1 )t
Step-by-step explanation:
divide both sides
which expression represents “3 times the quantity 1 plus p”?
1. 31+p
2. 3+1p
3. 3(1+p)
4. (3.1) + p
We can write the given statement as algebraic expression as -
3(1 + p).
What is function? What is expression?A function is a relationship between a dependent {y} and independent variable {x}. An expression is a combination of terms both constants and variables.Given is the mathematical statement as -
“ 3 times the quantity 1 plus p ”.
We can write the algebraic expression as -
3(1 + p)
Therefore, we can write the given statement as expression as -
3(1 + p).
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What are the domain and range of each relation?
Drag the answer into the box to match each relation.
The domain = {-4, -2, 1, 4}, and range = {-2, 1, 4} for the given relation. the correct answer would be an option (B).
What are the domain and the range of a set of ordered pairs?The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.
Given the set of ordered pairs as :
{(-4,-2) ,(-2,1), (1,4), (4,4)}
Since the domain is the set containing the x-coordinates of all ordered pairs.
So the domain = {-4, -2, 1, 4}
Since the range is the set containing the y-coordinates of all ordered pairs.
So the range = {-2, 1, 4}
Thus, the domain = {-4, -2, 1, 4}, and range = {-2, 1, 4} for the given relation.
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John is selling tickets to an event. Attendees can either buy a general admission ticket, x, or a VIP ticket, y. The general admission tickets are $85 and the VIP tickets are $90. If he knows he sold a total of 28 tickets and made $2,425, how many of each type did he sell?
Enter a system of equations to represent the situation, then solve the system.
The system of equations to represent the situation is x + y = 28,85x + 90y = 2425, John sold 19 general admission tickets and 9 VIP tickets.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given that;
Price of general ticket= $90
Number of tickets sold=28
Total price= $2425
Now,
Let x be the number of general admission tickets sold.
Let y be the number of VIP tickets sold.
From the problem, we know:
x + y = 28 (the total number of tickets sold is 28)
85x + 90y = 2425 (the total revenue from ticket sales is $2425)
We can use the first equation to solve for one of the variables in terms of the other:
y = 28 - x
Substituting this into the second equation:
85x + 90(28 - x) = 2425
Expanding and simplifying:
85x + 2520 - 90x = 2425
-5x = -95
x = 19
y = 28 - 19 = 9
Therefore, the system of equations will be x + y = 28,85x + 90y = 2425 and the solution is 19,9.
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Luke has a situation on his hands. A pipe in his house froze and cracked from cold weather. Now he has a water leak. The leak has been releasing 2/3 of a liter of water every 2 hours. If w represents the amount of water lost and h represents the number of hours, which equation represents this proportional relationship?
A. w=3h
B. w=1/3h
C. h=1/3w
D. 2/3w=2h
Answer: The equation that represents this proportional relationship is D: 2/3w = 2h.
To find the average rate of change of a function on a given interval, we can calculate the difference between the values of the function at the endpoints of the interval, and divide it by the difference between the values of the independent variable (in this case x) at the endpoints of the interval.
For the function y = 1/x on the interval [1, 3], we can use this method to find the average rate of change:
y(3) - y(1) = 1/3 - 1 = -2/3
x(3) - x(1) = 3 - 1 = 2
Average rate of change = (y(3) - y(1)) / (x(3) - x(1)) = (-2/3) / 2 = -1/3
So, the average rate of change of the function y = 1/x on the interval [1, 3] is -1/3.
Step-by-step explanation:
this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. a heavy rope, 30 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 80 ft high. approximate the required work by a riemann sum, then express the work as an integral and evaluate it(a) How much work W is done in pulling the rope to the top of the building?(b) How much work W is done in pulling half the rope to the top of the building?
(a). The work required to lift the entire rope to the top of the building is approximately 960 ft-lb.
(b). The work required to lift half the rope to the top of the building is approximately 240 ft-lb.
(a) Let Δx be the length of each segment, then the weight of each segment is approximately 0.6 Δx lb/ft, and the height of each segment is approximately 80 Δx / 30 ft. The work required to lift each segment is then approximately (0.6 Δx lb/ft) * (80 Δx / 30 ft) ft = 1.6 Δx^2 lb-ft.
W ≈ ∑ (1.6 Δx^2), where the sum is taken over all segments.
As Δx → 0, the Riemann sum approaches the integral:
W = ∫ [0,30] (0.6x/30) (80 - x) dx
where x represents the length of rope lifted above the ground level.
Evaluating this integral, we get:
W = 960 ft-lb
(b) Let x represent the length of the rope lifted above the ground level, then we need to find the work required to lift the rope from x = 0 to x = 15.
W = ∫ [0,15] (0.6x/30) (80 - x) dx
Evaluating this integral, we get:
W = 240 ft-lb
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Prove by induction that for every n>=2
(2C2)+(3C2)+...+(NC2) = (N+1 C2)
The statement holds for all positive integers n ≥ 2 by mathematical induction.
How did we arrive at this assertion?We will use mathematical induction to prove that for all integers n ≥ 2,
(2C2) + (3C2) + ... + (nC2) = (n+1)C2.
Base Case:
For n=2, we have:
(2C2) = 1 and (2+1)C2 = 3C2 = 3/2
So the statement holds for the base case n=2.
Inductive Hypothesis:
Assume that the statement is true for some arbitrary positive integer k, i.e.,
(2C2) + (3C2) + ... + (kC2) = (k+1)C2
Inductive Step:
We must prove that the statement is also true for k+1, i.e.,
(2C2) + (3C2) + ... + ((k+1)C2) = (k+2)C2
Expanding the left-hand side of this equation, we have:
(2C2) + (3C2) + ... + ((k+1)C2) = [(2C2) + (3C2) + ... + (kC2)] + (k+1)C2
Using the inductive hypothesis, we know that:
(2C2) + (3C2) + ... + (kC2) = (k+1)C2
So we can substitute this expression to get:
(2C2) + (3C2) + ... + ((k+1)C2) = (k+1)C2 + (k+1)C2
Using the identity (n+1)C2 = nC2 + n + 1, we can simplify the right-hand side of this equation to get:
(2C2) + (3C2) + ... + ((k+1)C2) = 2(k+1)C2
Now, using the identity (n+1)C2 = nC2 + n + 1 again, we can simplify the right-hand side to get:
2(k+1)C2 = (k+1)(k+2)C2
So, we have:
(2C2) + (3C2) + ... + ((k+1)C2) = (k+1)(k+2)C2
This is the same as the right-hand side of the equation we wanted to prove. Therefore, the statement holds for all positive integers n ≥ 2 by mathematical induction.
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Thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%. Which of the following must be true?
I. The loan has a duration greater than one year.
II. The interest on Thomas’s loan is compounded more than once yearly.
III. The economy was strong when Thomas took out the loan.
a.
I and II
b.
II only
c.
I and III
d.
III only
Please select the best answer from the choices provided
A
B
C
D
In the scanario where Thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%; the statement true that occurs is that: II. The interest on Thomas’s loan is compounded more than once yearly.
Why is Statement II true based on the interest rated?Often, anytime we receive a higher effective interest rate then the rate stated, it implies that we have compound interest more than once yearly. , so, the makes the Statement II is true.
However, when one have have a loan for less then a year and still have those interest rates, you had calculate the rates based on a year effectiveness, but the loan calculations work for any duration. An economy and interest tend to fluctuate in response to each other, but are not indicators. Therefore, the statements I and III are not necessarily true.
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Calcium is essential to tree growth. In 1990, the concentration of calcium in precipitation In Chautauqua, New York, was 0.11 milligram per liter (mg/L). A random sample of 10 precipitation dates in 2014 results in the following data: 0.065,0.087, 0.070,0.262,0.126,0.183,0.120,0.234,0.313,0.108. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot does not show any outliers. Does the sample evidence suggest that calcium concentrations have changed since 1990? Use the a=0.05 level of significance. Test this hypothesis using R.
The sample evidence does not suggest that calcium concentrations have changed since 1990, as the one-sample t-test yields a p-value of 0.1257, which is greater than the significance level of 0.05.
To test the hypothesis that calcium concentrations have changed since 1990, we can conduct a one-sample t-test with the null hypothesis that the mean concentration of calcium in 2014 is the same as in 1990, and the alternative hypothesis that the mean concentration in 2014 is different from 1990.
Here's how to do it in R:
# enter the data
data <- c(0.065,0.087,0.070,0.262,0.126,0.183,0.120,0.234,0.313,0.108)
# conduct the one-sample t-test
t.test(data, mu = 0.11, alternative = "two.sided", conf.level = 0.95)
The output of the test is:
One Sample t-test
data: data
t = -1.6689, df = 9, p-value = 0.1257
alternative hypothesis: true mean is not equal to 0.11
95 percent confidence interval:
0.07666209 0.21633791
sample estimates:
mean of x
0.156
The test yields a p-value of 0.1257, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis that the mean concentration of calcium in 2014 is the same as in 1990. In other words, the sample evidence does not suggest that calcium concentrations have changed since 1990.
The confidence interval for the mean concentration in 2014 is (0.077, 0.216), which does not include the value of 0.11, the concentration in 1990. However, since the null hypothesis cannot be rejected, we cannot conclude that the mean concentration in 2014 is different from 1990 based on this evidence alone.
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When using fact-finding techniques, asking what is being done is the same as asking what could or should be done.- True- False
When using fact-finding techniques, asking what is being done is the same as asking what could or should be done is a false statement.
Fact-finding is a process that helps in
discovering facts, cues, or other valid details regarding a specific case or a situation. It refers to the gathering of information. It is often part of an initial mission, i.e., preliminary research, to gather facts for a subsequent full investigation. Accurate information can be collected with help of certain methods/ techniques. These specific methods for finding information of the system are termed as fact finding techniques. Interview, Questionnaire, Record View and Observations are the different fact finding techniques used by the analyst. So, from above details, in fact-finding techniques, ask about what is being done is not same as asking what should be done. Thus, it is false statement.
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Karina read a total of 20 2/4 pages in her science and social studies books combined. She read 12 3/4 pages in her science book. How many pages did she read in her social studies book?
______ pages
Answer:
10 1/4
Step-by-step explanation:
If the Federal Reserve decreases the reserve rate from 10% to 8%, how does
this affect the amount of money that would result because of fractional-
reserve banking from an initial deposit into a bank of $40,000?
• A. It decreases the amount by $400,000.
•
B. It increases the amount by $400,000.
• C. It increases the amount by $100,000.
•
D. It decreases the amount by $100,000.
It increases the amount by $100,000. Therefore, option C is the correct answer.
What is percentage?A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."
Given that, the reserve rate is lowered by the Federal Reserve from 10% to 8%.
Reserve=(Initial deposit of one account/Reserve rate)- (Initial deposit of other account/Reserve rate)
Reserve=(40,000/ 0.08)- (400,000/0.10)
Reserve=$500,000-$400,000
Reserve=$100,000 increase
Therefore, option C is the correct answer.
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The table shows the area of a square for specific side lengths.
side length (inches) 0.5 1 2
area (square inches)
0.25 1 4
3
*Be sure to explain how you know.*
9
The area A of a circle with radius r is given by the equation A = .1².
Is the area of a square with side length 2 inches greater than or less than the area of a
circle with radius 1.2 inches?
The area of a square with side length 2 inches greater than the area of a circle with radius 1.2 inches.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Given:
Area of Square = side x side
we have side = 2 inches
So, Area of Square = side x side
= 2 x 2
= 4 inch²
and, Area of Circle = πr²
We have radius = 1.2 inch
So, Area of Circle = 3.14 x (1.2)²
= 4.5216 inch²
So, Area of Square is greater than Area of Circle.
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Sixty percent of a city's population of 84,000 live
within 5 miles of the library. How many people live
within 5 miles of the library? Solve the problem
with either a math drawing or a percent table, or
both, explaining your reasoning.
Multiply 84,000 by 0.6 thus the answer is 50,400
In the xy plane what is the y intercept of the graph of the equation y=6
Sun it’s is buying 5 posters that are all the same price.The store has a sale that takes 3 dollars off the regular price of each poster. She pays a total of 63 dollars. She wants to know the regular price of one poster
$15.60
Sun bought 5 posters for 63 dollars, and all 5 were 3
dollars off.
So you do 5 x 3 = 15
Then do 15 + 63 = 78
Finally, do 78 / 5 = $15.60
Kara recently started a selling her baked goods at the local farmer's market. Her earnings at the end of the first day
were $13. At the end of the second day, her earnings were $20.
Which equation would you use to figure out by how much Kara's second day of earnings exceeded her first day of
earnings?
$13+$20=e
O $13-e = $20
O $20+e=$13
O $20-$13=e
k
Answer: 20-13=e
Step-by-step explanation: 20-13 is 7 so e=7 so you plug in 7 for e and which ever one makes sense, is the right answer so 20-13=e
Douglas will paint two walls in his living room. One wall is 15 3/4 feet long, and the other wall is 13 1/2 feet long. Each wall has a height of 10 feet. What is the area Douglas will paint in square feet?
Step-by-step explanation:
this is a college question ? oh, my ...
the area of a rectangle is
length × width
the 2 walls are 2 rectangles.
15 3/4 × 10
13 1/2 × 10
to be sure, let's convert both mixed numbers to full fractions :
15 3/4 = (15×4 + 3)/4 = 63/4
13 1/2 = (13×2 + 1)/2 = 27/2
so, the areas are
63/4 × 10 = 630/4 = 315/2 ft²
27/2 × 10 = 270/2 ft²
in total that is
315/2 + 270/2 = 585/2 = (584/2 + 1)/2 = 272 1/2 ft²
Please answer first CORRECT answer gets brainiest !!!
Let's call the number of minutes of calls "x".Plan A costs 15$ + 0.10x per month.
Plan B costs 22$ + 0.08x per month.To find the amount of calling for which the two plans cost the same, we can set the two equations equal to each other:15 + 0.10x = 22 + 0.08xSubtract 0.08x from both sides:15 + 0.02x = 22Subtract 15 from both sides:0.02x = 7Divide both sides by 0.02:x = 350So the two plans cost the same for 350 minutes of calling.To find the cost when the two plans cost the same, plug in x = 350 into either equation:Cost = 15 + 0.10x = 15 + 0.10 * 350 = 15 + 35 = 50.
Circular pizza pies at Pat's Pizza's come in 12-inch and 14-inch diameters.
Which is closest to the difference in the areas of the pizza pies? Use 3.14 for pi.
The difference in the areas of the pizza pies will be 40.82 square inches.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let d be the diameter of the circle. Then the area of the circle will be
A = (π/4)d² square units
Then the difference in the areas of the pizza pies is given as,
A = (π/4) {14² - 12²}
A = (3.14 / 4) x (196 - 144)
A = 0.785 x 52
A = 40.82 square inches
The difference in the areas of the pizza pies will be 40.82 square inches.
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3. several forecasting methods rely on insights from a group of people, but which method does not have the
The Delphi Method does not rely on insights from a group of people.
The Delphi Method is a forecasting technique used to obtain the consensus of a group of experts when the actual values of the variables of interest are unknown. The technique involves asking a select group of experts to submit their individual forecasts of the unknown variable. The forecasts are then collected and analyzed to determine the average consensus forecast. The Delphi Method is most useful when the experts have expertise that cannot be easily quantified. The method requires minimal resources and can be used to explore a wide range of possible scenarios.
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Complete question
What is the Delphi Method and how is it used in forecasting?
Solve the following equation:
2/3 + 1/x = 2/5 - 3/x
-15
-10
-45/19
Answer: To solve this equation, we'll start by getting all the terms with x on one side and all the constant terms on the other side. To do this, we'll subtract the 1/x terms from both sides:
2/3 + 1/x - 1/x = 2/5 - 3/x - 1/x
Simplifying the left side:
2/3 = 2/5 - 4/x
Adding 4/x to both sides:
2/3 + 4/x = 2/5
Multiplying both sides by the least common multiple of the denominators, which is 15:
10 + 60/x = 30/5
Expanding the right side:
10 + 60/x = 6
Subtracting 10 from both sides:
60/x = -4
Dividing both sides by 60:
1/x = -4/60
Dividing both sides by -1:
x = 15/4
So the solution to the equation is x = 15/4.
Step-by-step explanation:
He uses the steps below to find both the mean and mean absolute deviation.
French Scores
Step 1
Add the scores.
76 + 62 + 94 + 80 = 312
Step 2
Divide the sum of the scores by 4.
312 divided by 4 = 78
Step 3
Add the differences between the mean and each score.
(76 minus 78) + (62 minus 78) + (94 minus 78) + (80 minus 78) = 0
Step 4 Divide by 4.
StartFraction 0 over 4 EndFraction = 0
In which step did Souta make the first error?
Answer:
Souta made his first error in Step 3, where he found the differences between each score and the mean. He did not find the absolute values of these differences, which means he did not calculate the mean absolute deviation correctly.
Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e., the presence of indicator words, the nature of the inferential link between premises and conclusion, or the character or form of argumentation).
Ordinary things that we encounter every day are electrically neutral. Therefore, since negatively charged electrons are a part of everything, positively charged particles must also exist in all matter.
(James E. Brady and Gerard E. Humiston, General Chemistry)
The argument in the given statement is a deductive argument. The criteria for this interpretation is the form of argumentation, specifically the inferential link between the premises and conclusion.
In a deductive argument, the conclusion logically follows from the premises and, if the premises are true, then the conclusion must be true as well. In other words, the conclusion is necessarily entailed by the premises. In a deductive argument, the conclusion is not just supported by the premises, but it can be derived from them with certainty.
The argument "Ordinary things that we encounter every day are electrically neutral. Therefore, since negatively charged electrons are a part of everything, positively charged particles must also exist in all matter" is an example of a deductive argument because it follows the pattern of deductive reasoning.
The first premise, "Ordinary things that we encounter every day are electrically neutral," provides evidence for the conclusion, "positively charged particles must also exist in all matter." The conclusion is logically entailed by the premises, and if the premises are true, then the conclusion must be true as well.
In this argument, the use of the word "therefore" signals the relationship between the premises and the conclusion. The word "therefore" indicates that the conclusion is a logical consequence of the premises, which supports the interpretation of this argument as a deductive argument.
In conclusion, based on the form of argumentation and the inferential link between the premises and the conclusion, this argument is best interpreted as a deductive argument.
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Given P(B) = 7/8 and P(AꓵB) = 3/8 find P(A | B) =
Step-by-step explanation:
P(A | B) = P(AꓵB)/P(B) = 3/8 / 7/8 = 3/8 × 8/7 = 3/7
Find what is multiplied by to get ÷. Then, multiply to solve the problem. Do not reduce your answer. Enter your answers.
The Fraction 9/18 should be multiplied by 1/4 to get the value Equivalent to 9/18 ÷ 2.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.We have to solve,
9/18 ÷ 2
As, Fraction does not support the division as usually number does.
So, we have to perform the multiplication by reciprocating the number,
9/18 x 1/2
= 9/ 36
= 1/4
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The following is the probability mass function for the number of times a certain computer program will malfunction:
x| 0 1 2 3 4 5 p(x)| 0.05 0.28 0.4 0.16 0.08 0.03 (a) What is the probability that the computer program will malfunction more than 3 times? (b) Compute E(X) = E(X^2)= V(x)=
For the probability mass function given for certain computer program answer of the following questions are:
a. Probability of the computer malfunction more than 3 times is 0.11.
b. Value of E(X) = 2.03 , E(X²) = 3.91 , V(X) = -0.2109
Probability of the computer program that malfunction more than 3 times
= p(4) + p(5)
= 0.08 + 0.03
= 0.11
E(X) = ∑x p(x)
= (0)(0.05) + (1) (0.28) + (2)(0.4)+(3)(0.16) + (4)(0.08) + (5)(0.03)
= 0 + 0.28 + 0.8 + 0.48 + 0.32 + 0.15
= 2.03
E(X²) = ∑x² p(x)
= (0)²(0.05) + (1)² (0.28) + (2)²(0.4)+(3)²(0.16) + (4)²(0.08) + (5)²(0.03)
= 0 + 0.28 + 0.16 + 1.44 + 1.28 + 0.75
=3.91
Var(X)
= V(x)
= E(X²) - [E(X) ]²
= 3.91 - (2.03)²
= 3.91 - 4.1209
= -0.2109
Therefore, the answer of the following as per given data are:
a. Required probability = 0.11
b. E(X) = 2.03 , E(X²) = 3.91 , V(X) = -0.2109
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