Suppose X has an exponential distribution with lambda equals 5. Determine the following. Round the answers to 3 decimal places.a) Upper P left-parenthesis Upper X less-than-or-equal-to 0 right-parenthesis equalsb) Upper P left-parenthesis Upper X greater-than-or-equal-to 2 right-parenthesis equalsc) Upper P left-parenthesis Upper X less-than-or-equal-to 1 right-parenthesis equalsd) Upper P left-parenthesis 1 less-than Upper X less-than 2 right-parenthesis equalse) Find the value of x such that Upper P left-parenthesis Upper X less-than x right-parenthesis equals 0.05.
Answer:
Explained below.
Step-by-step explanation:
The random variable X follows an exponential distribution with λ = 5.
The probability density function of X is:
[tex]f_{X}(x)=\lambda\cdot e^{-\lambda\cdot x};\ 0<x<\infty[/tex]
[tex]P(X\leq x)=1-e^{-\lambda\cdot x}\\\\P(X\geq x)=e^{-\lambda\cdot x}[/tex]
(a)
Compute the value of P (X ≤ 0) as follows:
[tex]P(X\leq 0)=1-e^{-\lambda\cdot x}[/tex]
[tex]=1-e^{-5\times 0}\\\\=1-1\\\\=0[/tex]
Thus, the value of P (X ≤ 0) is 0.
(b)
Compute the value of P (X ≥ 2) as follows:
[tex]P(X\geq 2)=e^{-5\times 2}=4.54\times 10^{-5}\approx 0[/tex]
Thus, the value of P (X ≥ 2) is approximately 0.
(c)
Compute the value of P (X ≤ 1) as follows:
[tex]P(X\leq 0)=1-e^{-\lambda\cdot x}[/tex]
[tex]=1-e^{-5\times 1}\\\\=1-0.00674\\\\=0.99326[/tex]
Thus, the value of P (X ≤ 1) is 0.99326.
(d)
Compute the value of P (1 ≤ X ≤ 2) as follows:
[tex]P(1<X<2)=\int\limits^{2}_{1} {5\times e^{-5x}} \, dx \\\\=5\times [\frac{e^{-5x}}{-5}]^{2}_{1} \\\\=5\times [\frac{0-0.00674}{-5}]\\\\=0.0067[/tex]
Thus, the value of P (1 ≤ X ≤ 2) is 0.0067.
(e)
Compute the value of x such that P (X < x) = 0.05 as follows:
[tex]P(X<x)=0.05\\\\\int\limits^{x}_{0} {5\times e^{-5x}} \, dx =0.05\\\\5\times [\frac{e^{-5x}}{-5}]^{x}_{0} =0.05\\\\1-e^{-5x}=0.05\\\\-e^{-5x}=0.95\\\\-5x=\ln(0.95)\\\\-5x=-0.05\\\\x=0.01\\\\[/tex]
Thus, the value of x is 0.01.
m∠AXB = this is the question
Answer:
Need a figure or more information to answer this question
You don’t have ti explain just tell me if it’s true or not
Answer:
no its not true
Step-by-step explanation:
The function C(x)=20x+4,000 represents the cost to produce x number of items. How many items should be produced so that the average cost is less than $40?
Answer:
More than 200 items must be produced to keep the average cost below $40 per item.
Step-by-step explanation:
the degree of non constant zero polynomial is
Answer:
it is zero . zero is the degree of zero polnomial
The steps to convert 17/4 to a decimal
Answer:
4.25
Step-by-step explanation:
why 17/4 is divided and what comes out or back is divided
Shana bought 6.2 pounds of pecans and paid $56.00. About how much per pound did the pecans cost?
$5.00
$6.00
$8.00
$10.00
Answer:
D
Step-by-step explanation:
yo you guys think you could help me find the sum
Answer:
4m + 8n -4p
Step-by-step explanation:
Im pretty sure its that. Hope its right!
HELP THIS IS MY LAST MATH QUESTION PLEASE HELP MEEEE!
Answer:
length =6 2/3 option 2.......
1/x-x/6=2/3 how to answer this
Answer:
x = 0.1
Step-by-step explanation:
1/x - x/6 = 2/3
1/ x - 6/x = 2/3
6/x = 2/3
6x = 2/3
x = 0.1
Answer:
x = 0.2
Step-by-step explanation:
1/x - x/6 = 2/3
=> 1/x - x = 2/3 * 6
=> 1/x - x = 12/3
=> 1/x - x = 4
=> 1/x - x/1 = 4 (x = x/1 )
=> 1 - x/1 = 4 * x
=> -x/1 = 4x - 1
=> -x/1 -4x = -1
=> -5x/1 = -1
=> x = -1/-5
=> x = 0.2 (Because negative / negative = positive)
If I am wrong please tell me.
If my answer helped, kindly mark me as the brinliest!!
Thanks!!
Write in standard form.
- 3
3.11 X 10
I
Answer: -3.11 x 10^ 1
Step-by-step explanation: - 3
3.11 X 10 = -31.1, in decimal form -3.11 x 10^ 1
I
Find X to complete the following ratio. 12:5 = 24:X
Answer:
x = 10
Step-by-step explanation:
This is the answer because:
1) 12:5 is equivalent to the ration 24:10
2) This is because to get 24 you have to multiply 12 and 2 which is 24
3) Next, you have to do the same to the other side to make everything equal. Therefore, you have to multiply 5 with 2 which is 10.
4) Finally, your answer should be 24:10
Hope this helps! :D
what is 390,000×600÷5?
Answer:
46,800,000 thats the answer
Latoya drove 335 miles in 5 hours.
At the same rate, how long would it take her to drive 603 miles?
Answer:
It would take her 9 hours because she would be going 67mph
Step-by-step explanation:
335mph divided by 5 hours is 67mph
a high school had 740 students at the start of the year but then some students left the school after , that the school had 726 students .
if s = the number of students who left the school which mathematical sentence expresses the information above?
Answer:
I believe it's 726=740-S
Answer:
s = 740 - 14
Hope it helps u
solve the following : -6x(-2) =
Answer:
12
Step-by-step explanation: Just do 6 x 2
What is the range of h?
Answer:
Image?
Step-by-step explanation:
Answer:
where is the image
Step-by-step explanation:
Kai took five tests this semester. His scores are listed below.
92, 88, 90, 96, 84
What is the mean absolute deviation of Kai's test scores?
Answer: 16
Step-by-step explanation:
Find the mean absolute deviation of the data:
X : 92, 88, 90, 96, 84
Find the mean(m) of the data:
m = Σ(X) / n
n = number of samples
(92 + 88 + 90 + 96 + 84) / 5
m = 450 / 5
m = 90
Absolute Deviation of each value of the mean:
|x - m| :
|92 - 90| = 2
|88 - 90| = 2
|90 - 90| = 0
|96 - 90| = 6
|84 - 90| = 6
Σ|x - m| = 2 + 2 + 0 + 6 + 6 = 16
Answer:
3.2
Step-by-step explanation:
Given the area and perimeter find the length and width
In this table what is the domain of the function?
Answer:
c. D: {1, 2, 3, 4, 5}
Step-by-step explanation:
The domain of a function includes values of x that are in the given table of values of the given function.
The range, on the other hand, includes all set of values of y, given in the table of values.
Thus, for the table of values above:
Domain would be [1, 2, 3, 4, 5]
Range would be [a, b, c, d, e]
The domain of the function can be represented as:
D: {1, 2, 3, 4, 5}
what is the slop between (2,7) and (10,22) on fraction form
Answer:
m=15/8
Step-by-step explanation:
Slope intercept form- Y=mx+b
Slope- 15/8x
Y- intercept- (0,13/4)
Snow play ski park cost $35 entry fee and then $5 per hour. If you have $60, how long can you be at snow play ski park
For $60, you may spend four hours at Snow Play Ski Park.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Snow plays ski park costs a $35 entry fee and then $5 per hour. If you have $60
Let "x" be the hours you can play in the ski park
Since,
Addition charges = 35
Thus your total expenses to play x hours in the park = 5*x + 35
Since We have only 60$
So,
60 = 5x + 35
=> 5x = 25
=> x = 5
therefore, You can be at a snow play ski park for four hours for $60.
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
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On a circle with radius 12 m, what angle would subtend an arc with a length of 7 m?
Answer:
33.42
Step-by-step explanation:
just trust me
33.42 angle would subtend an arc with a length of 7 m.
How do you find the angle of an arc?The angle formed by the arc at the center of the circle is the angle of the arc. Indicated by. m A B ^, A, and B are the endpoints of the arc. You can use the arc length equation to find a measure of the arc angle.
For a circle, the arc length equation is θ times the radius of the circle. The equation for arc length in radians can be expressed as Arc length = θ × r, where θ is in radians. Arc length = θ × (π / 180) × r, where θ is in degrees and L = arc length. θ = central angle of the arc.
Learn more about the angle of an arc here: https://brainly.com/question/2005046
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least common factor of 12 and 22
132 is the least common multiple
Answer:
Least common multiple (LCM) of 12 and 22 is 132.Step-by-step explanation:
Half of the students in Max’s class volunteer at the local community center.Fifteen students do not volunteer.If there is 12 boys in Max’s class,how many girls are in his class
Find the average of the numbers 10 1/3 5 5/9 2 1/36 3 3/4
Answer:
47/48
Step-by-step explanation:
hope this helps
Answer: 2.58 i think
Step-by-step explanation: add up all the numbers and divide them by how many numbers they were
Which graph represents the function y - 3= 3/2 (x - 4)?
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
Yes it is A i did it rn
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answer:
it is 25 percent
Step-by-step explanation:
in a decimal it is 0.25
PQRS is a parallelogram, m∠P=106∘ , and m∠Q=(11x−14)∘ .
What is the value of x?
9514 1404 393
Answer:
8
Step-by-step explanation:
Adjacent angles of a parallelogram are supplementary, so ...
106 +(11x -14) = 180
11x = 88 . . . . . . subtract 92
x = 8 . . . . . . . . .divide by 11
What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47+ ...?
Answer:
[tex]\huge\boxed{18,475}[/tex]
Step-by-step explanation:
The terms of this sum make the arithmetic sequence.
The fomula of a sum of n terms of an arithmetic sequence:
[tex]S_n=\dfrac{[2a_1+(n-1)d]\cdot n}{2}[/tex]
We have
[tex]a_1=2\\d=17-2=32-12=47-32=15\\n=50[/tex]
Substitute:
[tex]S_{50}=\dfrac{[2\cdot2+(50-1)\cdot15]\cdot50}{2}=(4+49\cdot15)\cdot25=(4+735)\cdot25\\\\=739\cdot25=18,475[/tex]