Suppose we have three random variablesX, Yand Z, whereXN(0,4),YN(2,1), andZ= 2Y+1. AssumeXandYare independent. Answer the following questions.
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Question:
Suppose we have three random variablesX, Yand Z, whereXN(0,4),YN(2,1), andZ= 2Y+1. AssumeXandYare independent. Answer the following questions.
(a) FindE[Z] and Var[Z].
(b) Find Corr(Y, Z).
(c) Find Cov(X,2XY2+ 3Z).
(d) Find the distribution ofX+Y+Z.
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