Let X and Y be two independent Bernoulli( 1/2 ) random variables. Define random variables U...

Question

Question

Let X and Y be two independent Bernoulli( 1/2 ) random variables. Define random variables U and V by

U = X + Y and V = | (X - Y) | (abs. value)):

(a) Find the joint probability mass function of (U, V ).

Hints: note that U and V are taking integer values in {0, 1, 2} and {0, 1}, respectively.

(b) Determine the covariance Cov(U, V ):

(c) Find Var(U), Var(V ) and determine the correlation coeffcient p(U, V ):

math Statistics-And-Probability

Answer 1

Answer #1

Answer 2

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