7.5 Sums and Differences of Independent Random Variables http://www.ck12.org Contents
7.5 Sums and Differences of Independent Ran-
dom Variables
Learning Objectives
- Construct probability distributions of random variables.
- Calculate the mean and standard deviation for sums and differences of independent random variables.
Introduction
In previous lessons, you learned that sampling is a way of estimating a parameter of a population by selecting data
from that population and a way of computing the chance of obtaining a specified outcome from a sample given
a specific population. In Fort McMurray, Alberta, better known as “Fort McMoney” because of the oil industry,
housing is becoming a rare commodity. Suppose you are a recent winner of a lottery and you decide to invest your
winnings in a housing project for this city. Your plan is to build 500 single-family homes. Before you begin, there are
some facts that you need to know so that the houses will be a quick sell and you can turn a profit for your investment.
One bit of information that you would like to ascertain is how many televisions each family will have so you will
know how many cable hook-ups to install in each household. Short of conducting a survey, how will you determine
a solution to this problem?
Probability Distributions from Data
To begin, you should contact the local cable provider in the city and ask them to provide you with a record of the
distribution of cable hook-ups per household that are currently on their books. Suppose they release this data:
TABLE7.5:
Hook-ups per Household Proportion of Households
0 0. 092
1 0. 328
2 0. 380
3 0. 142
4 0. 058