PROBLEMS
Simple Random Variable
5.1 Let X be a Laplace random variable with parameters 
. Define the mapping
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Write an expression for simple random variable Y and give its pmf.
5.2 Demonstrate that the binomial random variable is a simple random variable.
5.3 Partition the real line 
into the following three intervals: 
, (0, 2], and 
, and define
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where X is the standard Gaussian random variable. Write an expression for the simple random variable and Y give its pmf.
Expectation
5.4 (a) Show that if X is a nonnegative discrete random variable with 
, then P(X = 0) = 1. (b) Repeat part (a) with 
for P(X = 1) = 1.
5.5 Derive for the binomial random variable with parameters {N, p
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