UNIT 8 Discrete Probability Distributions

Intro Activity Summary (Ch 4 Review) HHHH HHTT THHT TTTT HHHT HTHT TTTH 2x2x2x2 = HHTH HTTH TTHT 16 outcomes HTHH THTH THTT THHH TTHH HTTT

Intro Activity Summary (Ch 3 Review) Possible Outcomes Frequency R.F. C.F C.R.F 1 2 3 4

We have already discussed that a variable is a characteristic or attribute that can assume different values (eye color, height, weight, etc.). Because we will now be working with variables associated with probability, we call them random variables. A random variable is a variable (typically represented by X) whose values are determined by chance. Chapter 1 review: Discrete variable have values that can be counted. Continuous variables are obtained from data that can be measured rather than counted. A probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values.

TTT TTH THT HTT HHT HTH THH HHH Let’s look at flipping 3 coins simultaneously. List the outcomes and their probabilities: TTT TTH THT HTT HHT HTH THH HHH Now let’s say that we are only interested in the number of heads. We would let X be the random variable for the number of heads. No heads One Head Two Heads Three heads TTT TTH THT HTT HHT HTH THH HHH

Number of heads X 1 2 3 Probability P(X) We end up with a probability distribution that looks like this: Number of heads X 1 2 3 Probability P(X) We can also represent probability distributions graphically by representing the values of X on the x axis and the probabilities P(X) on the y axis.

Two requirements for a probability distribution. The sum of the probabilities of all the events in the sample space must equal 1; that is, The probability of each event in the sample space must be between or equal to 0 and 1; that is,

Determine whether each distribution is a probability distribution. X 5 10 15 P(X) X 5 10 15 20 P(X) X 5 10 P(X) 0.5 0.3 0.4 X 5 10 15 P(X) -1.0 1.5 0.3 0.2

Finding the mean, variance, and standard deviation for a discrete random variable.

The mean of a random variable with a discrete probability distribution is The formula for the variance of a probability distribution is The standard deviation of a probability distribution is

Find the mean, variation, and standard deviation for the number of spots that appear when a die is tossed. X 1 2 3 4 5 6 P(X)

The probability that 0, 1, 2, 3, or 4 people will be placed on hold when they call is 18%, 34%, 23%, 21% and 4% respectively.

Pgs. 230-231 #19 – 24 all. Write the probability distribution in standard form, graph it, find the mean, and find the standard deviation.