Math 362 - Computer Lab #5 - Fall 2002

Introduction to Probability Theory

Computer Lab 5: The expectation of a random variable


In this lab, we will use large random samples as well as plots of p.m.f.'s and p.d.f.'s to estimate the mean of common random variables.

  1. The Bernoulli random variable

  2. The binomial random variable

  3. Consider a binomial random variable X with n = 5 and p = 0.75.

  4. The hypergeometric random variable
  5. Recall that the random variable giving the number of "successes" when n drawings without replacement are made from a pool of N items, m of which are "successes" and N-m of which are "failures" is hypergeometric. Consider a hypergeometric random variable with N = 20, m = 15 and n = 6.


  6. The normal random variable
  7. This continuous random variable is extremely important in probability theory because of the central limit theorem which, loosely speaking, states that many random phenomena empirically obey a normal distribution, at least approximately. A normal distribution is specified by two parameters, its mean l and its standard deviation s. The goal of this section is to explore how the p.d.f. changes when these two parameters are varied.

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