Simple Random Variable

5.1 Let X be a Laplace random variable with parameters . Define the mapping

(5.373) Numbered Display Equation

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

(5.374) Numbered Display Equation

where X is the standard Gaussian random variable. Write an expression for the simple random variable and Y give its pmf.


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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