Chapter 6 Discrete Probability Distributions Ch 6.1 ...

Chapter 6 Discrete Probability Distributions

Ch 6.1 Discrete Random Variables

Objective A: Discrete Probability Distribution

A1. Distinguish between Discrete and Continuous Random Variables

Example 1: Determine whether the random variable is discrete or continuous. State the possible values

of the random variable.

(a) The number of fish caught during the fishing tournament.

(b) The distance of a baseball travels in the air after being hit.

A2. Discrete Probability Distributions

1

Example 1: Determine whether the distribution is a discrete probability distribution. If not, state why.

Example 2: (a) Determine the required value of the missing probability to make the distribution a

discrete probability distribution.

(b) Draw a probability histogram.

Objective B: The Mean and Standard Deviation of a Discrete Random Variable

2

Example 1: Find the mean, variance, and standard deviation of the discrete random variable x .

?x

(a) Mean ? =

--->

Use the definition formula

¦Ò x2 =

x

0

1

2

3

4

x ? P( x)

P( x)

0.073

0.117

0.258

0.322

0.230

x

0

1

2

3

4

(b) Variance

¡Æ [ x ? P( x)]

¡Æ [( x ? ? )

x

2

? P( x)]

Formula (2a) in the textbook

P( x)

0.073

0.117

0.258

0.322

0.230

3

(c ) Variance --->

Use the computation formula

¦Ò x2 =

x

0

1

2

3

4

¡Æ[ x

2

? P( x)] ? ? x 2

Formula (2b) in the textbook

P( x)

0.073

0.117

0.258

0.322

0.230

Objective C : Expected Value

( x)

The mean of a random variable is the expected value, E=

¡Æ [ x ? P( x)] , of the probability

experiment in the long run. In game theory x is positive for money gained and x is negative for

money lost.

Example 1: A life insurance company sells a $250,000 1-year term life insurance policy to a 20year-old male for $350. According to the National Vital Statistics Report, 56(9),

the probability that the male survives the year is 0.998734. Compute and interpret

the expected value of this policy to the insurance company.

Example 2: Shawn and Maddie purchase a foreclosed property for $50,000 and spend an

additional $27,000 fixing up the property. They feel that they can resell the

property for $120,000 with probability 0.15, $100,000 with probability 0.45,

$80,000 with probability 0.25, and $60,000 with probability 0.15.

Compute and interpret the expected profit for reselling the property.

4

Chapter 6.2 The Binomial Probability Distribution

Objective A : Criteria for a Binomial Probability Experiment

The binomial probability distribution is a discrete probability distribution that obtained from a

binomial experiment.

Example 1: Determine which of the following probability experiments represents a binomial

experiment. If the probability experiment is not a binomial experiment, state why.

(a) A random sample of 30 cars in a used car lot is obtained, and their mileages

recorded.

(b) A poll of 1,200 registered voters is conducted in which the repondents are asked

whether they believe Congress should reform Social Security.

Objective B : Binomial Formula

Let the random variable x be the number of successes in n trials of a binomial experiment.

5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download