1. Probability Distributions Section 7.6

2. Definitions Random Variable: values are numbers determined by the outcome of an experiment. (rolling 2 dice: rv’s  2 through 12) Probability Distribution: function which maps each value of a rv onto its probability. Relative Frequency: Looks like a probability distribution, but in an experiment

3. Expected Value Weighted average! Let be a probability distribution. The mean (or expected value) μ (mu) of the distribution is

4. Example 1 Just for these notes, an author rolled two normal dice 9 times with the following sums: 6, 10, 11, 10, 9, 9, 12, 7, 9. Mean? Give the percent error between the mean and the expected value. x23456789101112 P(x)1/361/181/121/95/361/65/361/91/121/181/36 x23456789101112 P(x) =7 =31.7% 83/ 9 = 9.222

5. Example 2 There is a family with 4 children. Let the random variable of the distribution stand for the number of boys. a.What is the domain of the RV? b.Find the probability for each value of the rv c.Construct a histogram of the probability distribution. d.Find the expected value of the distribution.

6. Example 2 There is a family with 4 children. Let the random variable of the distribution stand for the number of boys. a.What is the domain of the RV? {0, 1, 2, 3, 4}

7. Example 2 There is a family with 4 children. Let the random variable of the distribution stand for the number of boys. b. Find the probability for each value of the rv X01234 P(X)1/164/166/164/161/16

8. Example 2 c. Construct a histogram of the probability distribution. X01234 P(X)1/164/166/164/161/16

9. Example 2 d. Find the expected value of the distribution. 0(1/16) + 1(4/16) + 2(6/16) + 3(4/16) + 4(1/16) = 2 X01234 P(X)1/164/166/164/161/16

10. Homework Pages 461 – 462 3 – 6, 8 – 9 13 – 14