Question
5. Suppose X; Y , and Z are iid with a Ber(1=4) distribution. Dene U = X + Y and V = Y=(1 + Z).
5. Suppose X; Y , and Z are iid with a Ber(1=4) distribution. Dene U = X + Y and
V = Y=(1 + Z).
(a) Specify the joint pmf of U and V .
(b) Give E[U jX].
(c) Calculate P(U > 1 j V < 1=2).
(d) Calculate the correlation coecient %(U; V ). Verify your answer with simulation and provide the code.
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Introductory Real Analysis
Authors: A N Kolmogorov, S V Fomin, Richard A Silverman
1st Edition
0486134741, 9780486134741
