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Discrete Probability Distributions

a. Confirm that this is a legitimate probability distribution by stating the conditions that must be satisfied and showing how they are satisfied

or

D. Based on this distribution, what is the probability that a tutor sees either three four students on a certain day?

Addition Rule for Disjoint Events : If E and F are disjoint (or mutually exclusive) events, then

2 Probability Distribution Requirements

P(E or F) = P(E) + P (F)

1. Each probability value must be between 0 and 1

2. The sum of the probabilities must be 1

=

P(3) + P (4)

Disjoint events: two events that cannot occur at the same time

Checking the 2 Requirements

1. Make sure your P(x) values are between

0 and 1

1

x

2

0

4

5

3

0.14

0.16

0.05

0.11

0.18

P(x)

0.36

=

P(1)+P(2)+P(3)

+P(4)+P(5)

2. Input the P(x) values into your calculator and make sure the sum is = 1

E. Based on this distribution, what is the probability that a tutor sees exactly 10 students on a certain day?

at least

C. Based on this distribution, what is the probability that a tutor sees two students on a certain day?

x

0

1

4

5

3

2

"At Least" : all probabilities larger than or equal to the given probability.

You cannot determine the probability of 10 students because x represents the number of students that a statistics tutor may see on a given day. So in this problem, the maximum number of students the tutor may see is 5.

=

since we were

given the number 2,

we include everything

larger than or equal to 2

P(2)+ P(3)+P(4)+P(5)

Answer is 0.

Practice Problem #1

This table is a probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students.

5

4

3

2

1

0

x

0.05

0.14

0.16

0.36

0.18

0.11

P(x)

b. Find the mean and the standard deviation of this distribution

Mean Formula

Standard Deviation

STA 282

Supplemental Instruction

Edited Version

= 2.19

=1.3243

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