Due 9/30/98:

In this assignment you are asked to derive certain formulae which can be found in the text. I want to see the derivations.

1.

Derive the formulae for the mean, variance and standard deviation for the discrete uniform distribution, for the binomial distribution, for the geometric distribution and for the Poisson distribution. You will find it helpful to read the proofs of Theorems 3.7, 3.8, and 3.11 in your text.

2.

Graph the probability mass function and the distribution function for a random variable with a binomial distribution with expected value of 4 and variance of 2.

3.

Graph the probability mass function and the distribution function for a random variable with a binomial distribution with expected value of 3 and variance of 2.

4.

Graph the probability mass function and the distribution function for a random variable with a hypergeomtric distribution with N = 26, n = 13 and r = 5.

5.

Graph the probability mass function and the distribution function for a random variable with a hypergeomtric distribution with N = 26, n = 13 and r = 6.

6.

Suppose that the random variable R has a geometric distribution, and H(z) = e^tz. Compute E[H(R)]. Be careful to indicate for which values of t E[H(R)] is defined.

7.

Suppose that the random variable R has a Poisson distribution, and H(z) = e^tz. Compute E[H(R)]. Be careful to indicate for which values of t E[H(R)] is defined.