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4. X1 and X2 have joint PMF Prob(X1 = x1, X2 0.15 x2) x2 0.15 0.15 0.15 0.20 0.20 (a) Compute the marginal distribution of X1. (b) Compute the marginal distribution of X2. (c) Compute the conditional distribution of X|X2. (d) Compute the conditional distribution of X2|X1. (e) Are X1 and X2 independent? Justify your answer.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

7. Consider the following system of equations, depending on the parameter k (k + 2)x1 + 8ri + x2 (k + 4).x2 = - 3k +3 12 Which of the following is true? (A) The system is consistent if and only if k -6. B) The system has unique solution if and only if k +0. C) The system has no solution if k = 1. D) The system has infinitely many solutions if and only if k = -6. E) None of the above.

Given independent random variables X and Y with E ( X )=80, σX=10 and E (Y)=85, σY =12 respectively, find the mean and variance of each of the following random variables.

a. W=4X-2Y

b. {X1 ,..., X 100} and {Y1, ...,Y 100} are independent draws from X and Y distributions.

W=y bar -x̅ 

 

c. {X1,..., X10} are independent draws from X distributions.

W =X1+,...,+X10

 

d. W=10X

You are given the joint pdf of the random  variables, X and Y

 

(a) What is the marginal distribution of X.

(b) What is the marginal distribution of Y

(c) Find the conditional distribution of X.

(d) Find E(X), where this is defined, what restrictions, if any, do we impose?

 

 

 

 

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