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CHAPTER 6 RANDOM VARIABLES

PART 1 – Discrete and Continuous Random Variables

OBJECTIVE(S): • Students will learn how to use a probability distribution to answer questions about possible values of a random variable. • Students will learn how to calculate the mean and standard deviation of a discrete random variable. • Students will learn how to interpret the mean and standard deviation of a random variable.

Random Variable –

Probability Distribution -

Discrete Random Variable -

The probabilities of a probability distribution must satisfy two requirements:

a.

b.

Mean (expected value) of a discrete random variable

[pic]= E(X) =

=

1. In 2010, there were 1319 games played in the National Hockey League’s regular season. Imagine selecting one of these games at random and then randomly selecting one of the two teams that played in the game. Define the random variable X = number of goals scored by a randomly selected team in a randomly selected game. The table below gives the probability distribution of X:

Goals: 0 1 2 3 4 5 6 7 8 9

Probability: 0.061 0.154 0.228 0.229 0.173 0.094 0.041 0.015 0.004 0.001

a. Show that the probability distribution for X is legitimate.

b. Make a histogram of the probability distribution. Describe what you see.

0.25

0.20

0.15

0.10

0.05

0.00

0 1 2 3 4 5 6 7 8

c. What is the probability that the number of goals scored by a randomly selected team in a randomly selected game is at least 6?

d. Compute the mean of the random variable X and interpret this value in context.

NOTE: If the mean of a random variable has a non-integer value, but you report it as an...

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