Statistics: Principles and Methods, 7th Edition

5

Probability Distributions

1 Random Variables

2 Probability Distribution of a Discrete Random Variable

3 Mean (Expected Value) and Standard Deviation of a Probability Distribution

4 Successes and Failures—Bernoulli Trials

5 The Binomial Distribution

6 The Poisson Distribution and Rare Events

Rescue Service on a Lake

Student sailors and other boaters on Lake Mendota are protected by a boating rescue service. The relative frequencies from a long record for summer days leads to an approximate distribution of the number of rescues per day.

The distribution describes the randomness of daily rescue activity. For instance, on any given day, the most probable number of rescues is 2. The distribution can be the basis for decisions concerning manpower and the need for additional rescue boats.

A prescription for the probability model of an experiment contains two basic ingredients: the sample space and the assignment of probability to each elementary outcome. In Chapter 4, we encountered several examples where the elementary outcomes had only qualitative descriptions rather than numerical values. For instance, with two tosses of a coin, the outcomes HH, HT, TH, and TT are pairs of letters that identify the occurrences of heads or tails. If a new vaccine is studied for the possible ...