1. UNIT 8 Discrete Probability Distributions

2. 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

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

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.

5. 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

6. 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.

8. 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,

9. 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

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

11. 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

12. Find the mean, variation, and standard deviation for the number of spots that appear when a die is tossed. X
P(X)

14. 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.

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