2. If two random variables X and Y are independent, (a) their joint distribution equals the product of their conditional distributions (b) the marginal distribution of X equals the conditional distribution of X given Y (c) the marginal distribution of Y equals the conditional distribution of Y given X (d) b and c (e) a, b, and c

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4 Feb 2023

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Related questions

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

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

harlequingerbil370

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

Y=0 Y=1

X=0
X=1

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?