Write out your FULL name… first, middle and last.

a) Count how many letters are in your FULL name.

b) Count how many letters are in your first name.

Bluman, Chapter 5 1

Sec 5.2

Mean

Variance

Expectation

Bluman, Chapter 5 2

Bluman, Chapter 5 3

Test on chapters 4 and 5Wednesday Oct 30th

Review: Do you remember the following? The symbols for

VarianceStandard deviationMean

The relationship between variance and standard deviation?

Bluman, Chapter 5 4

5-2 Mean, Variance, Standard Deviation, and Expectation

MEAN: X P X

2 2 2

VARIANCE:

X P X

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Rounding Rule

The mean, variance, and standard deviation should be rounded to one more decimal place than the outcome X.

When fractions are used, they should be reduced to lowest terms.

Mean, Variance, Standard Deviation, and Expectation

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Chapter 5Discrete Probability Distributions

Section 5-2Example 5-5

Page #260

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Example 5-5: Rolling a DieFind the mean of the number of spots that appear when a die is tossed.

.

Bluman, Chapter 5

X P X 1 1 1 1 1 16 6 6 6 6 61 2 3 4 5 6

216 3.5

8

Chapter 5Discrete Probability Distributions

Section 5-2Example 5-8

Page #261

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Example 5-8: Trips of 5 Nights or MoreThe probability distribution shown represents the number of trips of five nights or more that American adults take per year. (That is, 6% do not take any trips lasting five nights or more, 70% take one trip lasting five nights or more per year, etc.) Find the mean.

.

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Example 5-8: Trips of 5 Nights or More

Bluman, Chapter 5

X P X

0 0.06 1 0.70 2 0.20

3 0.03 4 0.01

1.2

11

Chapter 5Discrete Probability Distributions

Section 5-2Example 5-9

Page #262

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Example 5-9: Rolling a DieCompute the variance and standard deviation for the probability distribution in Example 5–5.

.

Bluman, Chapter 5

2 2 2X P X

2 2 2 2 21 1 1 16 6 6 6

22 21 16 6

1 2 3 4

5 6 3.5

2 2.9 , 1.7

13

Chapter 5Discrete Probability Distributions

Section 5-2Example 5-11

Page #263

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Example 5-11: On Hold for Talk Radio

A talk radio station has four telephone lines. If the host is unable to talk (i.e., during a commercial) or is talking to a person, the other callers are placed on hold. When all lines are in use, others who are trying to call in get a busy signal. The probability that 0, 1, 2, 3, or 4 people will get through is shown in the distribution. Find the variance and standard deviation for the distribution.

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Example 5-11: On Hold for Talk Radio

Bluman, Chapter 5

2 2 2 2

22 2

0 0.18 1 0.34 2 0.23

3 0.21 4 0.04 1.6

2 1.2 , 1.1

16

0 0.18 1 0.34 2 0.23

3 0.21 4 0.04 1.6

Example 5-11: On Hold for Talk Radio

A talk radio station has four telephone lines. If the host is unable to talk (i.e., during a commercial) or is talking to a person, the other callers are placed on hold. When all lines are in use, others who are trying to call in get a busy signal.

Should the station have considered getting more phone lines installed?

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Example 5-11: On Hold for Talk Radio

No, the four phone lines should be sufficient.

The mean number of people calling at any one time is 1.6.

Since the standard deviation is 1.1, most callers would be accommodated by having four phone lines because µ + 2 would be

1.6 + 2(1.1) = 1.6 + 2.2 = 3.8.

Very few callers would get a busy signal since at least 75% of the callers would either get through or be put on hold. (See Chebyshev’s theorem in Section 3–2.)

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Expectation The expected value, or expectation, of

a discrete random variable of a probability distribution is the theoretical average of the variable.

The expected value is, by definition, the mean of the probability distribution.

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E X X P X

Chapter 5Discrete Probability Distributions

Section 5-2Example 5-13

Page #265

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Gain X

Probability P(X)

Example 5-13: Winning Tickets

One thousand tickets are sold at $1 each for four prizes of $100, $50, $25, and $10. After each prize drawing, the winning ticket is then returned to the pool of tickets. What is the expected value if you purchase two tickets?

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$98 $48 $23 $8 - $22

10002

10002

10002

1000992

1000

2 2 21000 1000 1000

99221000 1000

$98 $48 $23

$8 $2 $1.63

E X

Gain X

Probability P(X)

Example 5-13: Winning Tickets

One thousand tickets are sold at $1 each for four prizes of $100, $50, $25, and $10. After each prize drawing, the winning ticket is then returned to the pool of tickets. What is the expected value if you purchase two tickets?

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$100 $50 $25 $10 $02

10002

10002

10002

1000992

1000

2 2 21000 1000 1000

99221000 1000

$100 $50 $25

$10 $0 $1.63$2

E X

Alternate Approach

On Your Own:

Technology Step by Step page 269

Exercises 5-2 Page 267 #

3,9,13 and 15

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