4.1 Probability Distributions

Do you remember?

• Relative Frequency Histogram

1 - 5 6 - 10 11- 15 16-20 21-25 26-30 31-350

0.05

0.1

0.15

0.2

0.25

0.3

Relative Frequency Histogram

Random Variables

• X, has a single value for each outcome in an experiment

• When Rolling a 6 sided dice X could be equal to 1,2,3,4,5,6

Discrete Random Variables

• Have values separate from one another

• The number of calls made by a salesperson

Continuous Random Variable

• Have an infinite number of possible values in a continuous intervals

• The length of time a salesperson spent on the phone

Probability Distributions

• They show what the likelihood of all events in the sample space

Single Dice Rolled

Flipping 3 Coins

Now we Make One

• Make a probability distribution for the numbers of tails on 3 flips.

Expected Value

• If you repeated an experiment (lets say number of tails in 4 flips) many times, on average how many tails would you expect?

• Denoted E(X)= expected value

Expected Value

• What is the expected number of Tails when you flip a coin 3 times?

Committee of Women

• Suppose you want to select a committee consisting of three people. The group from which the committee members can be selected consists of four men and three women.• Make a probability histogram for this distribution

• Calculate the expected number of women on the committee.

Assignment

• Pg 151 #’s 1,4,5,6abcd,7,8,9,14