4. suppose that events a and b are conditionally independent given event c. suppose that p(c) > 0 and p(c c ) > 0. (a) are a and bc guaranteed to be conditionally independent given c? justify your answer. (b) are a and b guaranteed to be conditionally independent given c c ? justify your answer.

Answers

Answer 1

From the Conditional probability formula, if events A and B are conditionally independent given event C,

a) Yes, for A and Bᶜ guaranteed to be conditionally independent given C.

b) No, A and B guaranteed to be conditionally independent given Cᶜ.

Conditional probability represented by notation P(A|B) is read as the probability of event A occurring given that event B has occurred. We will use the definition of conditional probability and independent events to prove the required result. In conditional probability, we calculate the probability of an event and it is known that the other event has already occurred. The events A and B are conditionally independent for the given event C such that P( C) > 0 and P( Cᶜ ) > 0.

In case of independent, the probability of one event can't be effect the probability of a 2nd event, that is Probability of intersection of two events is product of individual probabilities

From the definition of conditional probability, for independent events A and B, P( (A∩B)| C) = P( A|C) P( B|C)

a) Using the properties of conditional probability, [tex]P( ( A∩B^c )| C) = P( A|C) P( B^c |C) \\ [/tex]

so, yes, A and B guaranteed to be conditionally independent given C.

b) Using the properties of conditional probability independent, P( (A∩B)| C) = P( A|C) P( B|C) but [tex]P( (A∩B)| C^ c ) ≠ P( A|C^c) P( B|C^c) \\ [/tex].

So, A and B are not guaranteed to be conditionally independent given Cᶜ.

Hence, the first statement is right but not second.

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Complete question:

4. suppose that events A and B are conditionally independent given event C. suppose that p(C) > 0 and p(Cᶜ ) > 0. (a) are a and bc guaranteed to be conditionally independent given c? justify your answer. (b) are a and b guaranteed to be conditionally independent given Cᶜ ? justify your answer.


Related Questions

what is 69% of 69 what is 69% of 69

Answers

Answer:

69% of 69 is 47.61 :)

What???? I think the person on the top is correct

i need help with this pls 20 points for the right answer

Answers

Answer:

hiiii

Step-by-step explanation:

sorry I have not idea like what garde are u I'm

Which of the following could be the side measures of a right triangle? *

1)6 ft, 5 ft, 4 ft

2)8 ft, 7 ft, 6 ft

3)10 ft, 8 ft, 6 ft

4)12 ft, 10 ft, 8 ft

Answers

Answer:

option 1

Step-by-step explanation:

please Mark me as brainlist

The set of side lengths that could represent a right triangle is

12 ft, 10 ft, and 8 ft.

Option D is the correct answer.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine which of the given sets of side lengths could represent a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

Using this theorem, we can check each of the given sets of side lengths to see if they satisfy this condition:

6 ft, 5 ft, 4 ft

6² + 5² = 36 + 25 = 61

4² = 16

Since 61 is not equal to 16, this set of side lengths does not represent a right triangle.

8 ft, 7 ft, 6 ft

8^2 + 7^2 = 64 + 49 = 113

6^2 = 36

Since 113 is not equal to 36, this set of side lengths does not represent a right triangle.

10 ft, 8 ft, 6 ft

10^2 + 8^2 = 100 + 64 = 164

6^2 = 36

Since 164 is not equal to 36, this set of side lengths does not represent a right triangle.

12 ft, 10 ft, 8 ft

12^2 + 10^2 = 144 + 100 = 244

8^2 = 64

Since 244 is equal to 64 + 180, this set of side lengths does represent a right triangle.

Therefore,

The set of side lengths that could represent a right triangle is 12 ft, 10 ft, and 8 ft.

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Which equation does the model below represent? pls help !

Answers

Answer:

the answer to this is d

Step-by-step explanation:

x-3=5

Find the area of the parallelogram. Round to the nearest hundredth if necessary.

Answers

Answer:

1424.81 square meters

Step-by-step explanation:

20.21 m * 70.5m = 1424.805 square meters

So then you round it to the nearest hundredth so then..

1424.81 square meters

Step-by-step explanation:

A of a parallelogram = Base ×height

= 20.21×70.5= 1424.805m

nearest hundreth = 1424.81 m

Using suitable identity find 5.62

− 0.32​

Answers

Answer:

5.62 - 0.32= 5.3 or 5.30

Step-by-step explanation:

say something so mean to me idc just say whats on your mind broskis

Answers

Answer:

Can grape juice be made into grapes?

Your so UGLY you turned medusa into stone.

Step-by-step explanation:

I said what was on my mind

I’m bored and wish I could hang out with a friend or something. Also you are more disappointing than an unsalted pretzel.


There are three rows of VIP seats in each section. Each row
has 12 seats and there are 16 sections. How many VIP seats
are there in all?

Answers

Answer:

576 I think

Step-by-step explanation:

3 x 12 x 16

Consider the equation: 1 4 x + 3y − 23 = 42 The variables are: The coefficients are: The constants are:

Answers

Answer:

The variables are: x and y

The coefficients are: 1/4 and 3

The constants are: -23 and 42

Step-by-step explanation:

Given equation:

1/4x + 3y − 23 = 42

The variables are: x and y

The coefficients are: 1/4 and 3

The constants are: -23 and 42

someone help me please quick?

Answers

if I'm not wrong the answer does seem to be 69

1,4,5 and 8 are congruent

2. Which of the following are solutions to - 2.7 + x = - 3.5?

Answers

Step-by-step explanation:

x = -4/5 = -0.8

Answer:

x = −0.8

Step-by-step explanation:

−2.7 + x = −3.5

1.) Simplify both sides of the equation

x − 2.7 = −3.5

2.) Add 2.7 to both sides

x − 2.7 + 2.7 = −3.5 + 2.7

AND BAYUM...

x = −0.8

~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope I helped!!!

GL :)

x2 = 36 solve for x please answer

Answers

Step-by-step explanation:

Given

x² = 36

x² =( +6)²

x = +6

Hope it will help :)

Answer:

x= 18

Step-by-step explanation:

Divide both sides by 2

2 and 2 cancel out

36/2=18

check that it fits

2 x 18=36

18 is correct

Hope this helps ^-^

what is the solution to d · -4=32​

Answers

Answer:

-8

Step-by-step explanation:

-4d=32

d=32/-4

d=-8

PLEASE PLEASE HELP ME!!!

Answers

I tried to show all work.

Answer:

majadoxkdkdkrjjdkaoxjxjdhuriqwlsnxbxjdiirkekrnrnrjhfuxueiejhrhd

Eqiuvalent expressions
5(x)(x)(x)(x)

Answers

Answer:

5x^4

Step-by-step explanation:

a right circular cylinder with a radius of 2.3cm and a height of 1.4cm has a total surface area of ​

Answers

Answer:

i think 6.44

Step-by-step explanation:

first the diameter is 4.6 then multiply the 4.6 with 1.4 and u obtaine 6.44 (note:iam not sure iam still in seven grade)

Convert: 7 qt.=________fl.oz

Answers

Answer:

224 fl.oz

Step-by-step explanation:

Please help.
Is Algebra.

Answers

Answer:

5. 2, 6. 18

Step-by-step explanation:

8-?= 6, ? = 2

?-11 = 7, ? = 18

How many fluid ounces are in 1 quart

Answers

1 quart is 32 fluid ounces

A box of dried fruit has 80 calories in 5 servings. How many calories are there per serving?

Answers

Answer:

16 calories per serving

Step-by-step explanation:

80/5=16 calories per serving

Answer:

16 calories per serving. Hope this helps

Step-by-step explanation:

a(b - 4) + c(b - 4)
can someone help me please!!!​

Answers

Answer:

(b−4)(a+c)

Step-by-step explanation:

Answer:

ab-4a+cb-4c

Step-by-step explanation:

a(b-4)+c(b-4)

ab-4a+cb-4c

Jazzy goes to bed 3 h after dinner.

Yesterday, she spent 1 1/2 h on her homework and 2/3 h on the telephone after dinner.

How much time does she have before bed time?


PLEASE SHOW YOUR WORK!!!

Answers

Answer:

It was easy

Step-by-step explanation:

11 x 2 = 22

3 x 2 = 6

22 x 6 = 132

The time Jazzy has before going to bed is  [tex]\frac{5}{6}[/tex] hour

The first step to take in determining the answer is to add the hours she spent on various activities she did after dinner

Sum of activities done after dinner = hours spent on homework + hours spent on the telephone

[tex]1\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex]

[tex]1\frac{3 + 4}{6}[/tex]

= [tex]1\frac{7}{6}[/tex]

=[tex]2\frac{1}{6}[/tex]  hours

Th second step is to subtract the total hours Jazzy spent on activities from the hours Jazzy has before going to bed after dinner

Time left before she goes to bed = time she has to go to bed after dinner - total hours spent before going to bed

3 - [tex]2\frac{1}{6}[/tex]  hours = [tex]\frac{5}{6}[/tex] hour

A similar question was solved here: https://brainly.com/question/18157047?referrer=searchResults

Find each angle measure.

Answers

Answer:

Step-by-step explanation:

1)140

2)70

answers:
1) 140
2) 70

What are the possible measures of the triangle’s sides? Select all that apply.

Answers

Answer:

since a whole triangle is 180 you can do 60×3

Answer:

Step-by-step explanation:

Whole triangle = 180°

90 + 60 + 30

What is the value of w?

Answers

AnswThe letter (W) is the symbol used to represent whole numbers. Whole numbers are counting numbers from 0 to infinity. The whole numbers (W): 0, 1, 2, 3, 4 . . . Notice that every natural number is a whole number.er:

Step-by-step explanation:

w + 48° = (w + 7°) + (w-27°)

48° = w + 7° - 27°

48 = w -20°

68° = w

What is the main idea of this text
Atkins agreed to testify against Manson in exchange for avoiding the death penalty. Her grand jury testimony led to Manson being arraigned for the murders on Dec. 11, 1969. Atkins later recanted her testimony, and her deal was revoked by the prosecutors [source: Steffens and Staples]. Linda Kasabian, who hadn't entered any of the houses or committed any murders, was granted immunity and testified for the prosecution during the trial.​

Answers

Answer:

the answer is Atkins agreeing to testify against Manson in exchange for avoiding the death penalty

find the perimeter of the rectangle​

Answers

Answer:

b. 14 cm

Step-by-step explanation:

To find the other side of the right triangle, use the Pythagorean theorem, a^2+b^2=c^2. The side is 4 cm, so 3+3+4+4=14 cm.

Solve the equation, and choose the type of solution you
found.
2x + 8 = 2(x + 4)

Answers

Answer:

All real numbers are solutions

Step-by-step explanation:

2x + 8 = 2(x + 4)

~Simplify right side

2x + 8 = 2x + 8

~Subtract 8 to both sides

2x = 2x

~Divide 2 to both sides

0 = 0

Best of Luck!

Answer: the answer is infinite

Step-by-step explanation: so first you need to distribute the 2 into the () and you would get 2x+8 and since it is the same on both sides it cancles eachother out therefore there is infinite answers

Justin won the track event with a time of
12.0683 seconds. Write this round this off
to the nearest hundredth.

Answers

Answer:

12.068

Step-by-step explanation: the nearest hundredth to 12.0683 is 12.068  because 3 is  below five

Which statement is true about the slope of the graphed line?

Answers

Answer:

B, the slope is positive.

Step-by-step explanation:

You can tell that the slope is positive because it is going upwards from left to right.

B) Positive slope. A trick to doing this is if you can draw a P shape based on the slope, it is positive. An N shape is negative.
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