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20 points We use E(-) and V(.) to denote a random variable's mean (or expectation) and...

Question:

20 points We use E(-) and V(.) to denote a random variables mean (or expectation) and variance, respectively. Given two discrete random variables X and Y, where X E 10,1 and Y E {0, 1}. The joint probability p(X,Y) is given in as follows: 0 1/10 2/10 X 1 3/10 4/10 (a) [10 points| Calculate the following distributions and statistics i. the the marginal distributions p(X) and p(Y) ii. the conditional distributions p( Y) and p(Y|X) v. the covariance between X and Y (b) [5 points] Are X and Y independent? Why? (c) [5 points] When X is not assigned a specific value, are E(Y|X) and V(Y|X) still constant? Why?

20 points We use E(-) and V(.) to denote a random variable's mean (or expectation) and variance, respectively. Given two discrete random variables X and Y, where X E 10,1 and Y E {0, 1}. The joint probability p(X,Y) is given in as follows: 0 1/10 2/10 X 1 3/10 4/10 (a) [10 points| Calculate the following distributions and statistics i. the the marginal distributions p(X) and p(Y) ii. the conditional distributions p( Y) and p(Y|X) v. the covariance between X and Y (b) [5 points] Are X and Y independent? Why? (c) [5 points] When X is not assigned a specific value, are E(Y|X) and V(Y|X) still constant? Why?

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