Homework Answers 5. a) discrete b) Continuous c) Continuous d) Discrete e) continuous 6. a) continuous b) Discrete c) Discrete d) Continuous e) discrete 7. yes; μ = 1.5; σ = .9 8. No 9. no 10. yes; μ = 0.6; σ = 0.7

Section 5.2 Random Variables

Homework Quiz Is the following a probability distribution? X P(x) .3 1 .3 1 .27 2 .14 3 .03 4 .21 5

How to use the Calculator TI-83 / TI-84 Computing Mean and Standard Deviation Enter the values of the random variable x in the list L1. Enter the corresponding probabilities in the list L2. Press STAT, select CALC option and choose 1-Var Stats Enter "L1,L2" and Press the ENTER key.

Building Onto Previous Knowledge Important Definition The expected value of a discrete random variable is denoted by E, and it represents the mean value of the outcomes. It is obtained by finding the value of Where have we seen this before?

A Little Clarification We can think of the mean as the expected value in the sense that it is the average value that we would expect to get if the trials could continue indefinitely. For example, an expected value of 3.2 girls is not meant to be interpreted as the number of girls in one trial will be equal to 3.2, but rather it means that among many such trials, the mean number of girls is 3.2

So how do we know what to expect? The Exciting Stuff So how do we know what to expect? Range Rule of Thumb Maximum usual value = Minimum usual value =

So how do we know what to expect? The Exciting Stuff So how do we know what to expect? Rare Event Rule x successes among n trials is an unusually high result when P(x or more) ≤ 0.05 x successes among n trials is an unusually low results when P(x or fewer) ≤ 0.05

Now Apply It! Based on data from CarMax. Com when a car is randomly selected the number of bumper stickers and the corresponding probabilities are 0 (0.824), 1(0.083), 2 (0.039), 3 (0.014), 4 (0.012), 5 (0.008), 6 (0.008), 7 (0.004), 8 (0.004), and 9 (0.004). Does the given information describe a probability distribution? Is it unusual for a car to have more than one bumper sticker?

Now Apply It! In the Illinois Pick 3 lottery game, you pay $0.50 to select a sequence of three digits, such as 233. If you select the same sequence of three digits that are drawn, you win and collect $250. How many different selections are possible? What is the probability of winning? Determine the expected value of your earnings.

Now Apply It! There is a 0.9968 probability that a randomly selected 50- year-old female lives through the year (based on data from the U.S Department of Health and Human Services). A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50,000 as a death benefit. If she purchases this policy, what is the expected value of the insurance company’s profit?

Homework Pg. 216-217 #16, 17, 18, 28, 29