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# h3 - Stat 5101(Geyer Fall 2011 Homework Assignment 3 Due...

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Stat 5101 (Geyer) Fall 2011 Homework Assignment 3 Due Wednesday, September 28, 2011 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 3-1. Suppose that f is a PMF on a sample space S , suppose X and Y are random variables in this probability model. Prove the following statements. (a) E ( X + Y ) = E ( X ) + E ( Y ). (b) If X ( s ) 0 for all s S , then E ( X ) 0. (c) If Y ( s ) = a for all s S , then E ( XY ) = aE ( X ). (d) If Y ( s ) = 1 for all s S , then E ( Y ) = 1. Do not use the axioms (these are the axioms). The problem is to prove that these statements follow from our earlier deﬁnition of PMF and expectation. 3-2. Suppose X has the uniform distribution on the set { 1 , 2 , 3 , 4 } , and suppose Y = X 2 . (a) Calculate E ( X ). (b) Calculate

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h3 - Stat 5101(Geyer Fall 2011 Homework Assignment 3 Due...

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