1. Chapter 7.2

2. The __________ of a discrete random variable, X, is its _________ _____________. Each value of X is weighted by its probability. To find the mean of X, ____________ each value of X by its probability, then _________ all the products. The mean of a random variable X is called the ___________ ______________ of X

3. Choose an American household at random and let the random variable X be the number of persons living in the household. If we ignore the few households with more than 7 inhabitants, the probability distribution of X is as shown below. What is the expected value of the number of inhabitants of an American household? Inhabitant s 1234567 Probability.25.32.17.15.07.03.01

4. Let’s look back at the Apgar Scores... Compute the mean of the random variable X and interpret this value in context.

5. If X is a discrete random variable with mean μ, then the variance of X is The standard deviation of X is the ___________________ of the _______________.

6. Let X be the number of courses for which a randomly selected student at a certain university is registered. What is the mean and standard deviation of this distribution? Now, interpret the standard deviation in context. X1234567 P(X).02.03.09.25.40.16.05

7. Consider the random variable X=Apgar Score Compute the standard deviation of the random variable X and interpret in context.

8. If a player rolls two dice and gets a sum of 2 or 12, he wins $20. If he gets a 7, he wins $5. The cost to roll the dice one time $3. Is this game fair? Let x represent the profit your earn.

9. The probability that 0, 1, 2, 3 or 4 people will seek treatment for the flu during any given hour at an emergency room is shown in the following distribution. a) What is the mean of X? b) What is the variance and standard deviation of X? X01234 P(X)0.130.250.320.240.06

11. Rules for Means: If X is a random variable and a and b are fixed numbers, then Rules for Variances: If X is a random variable and a and b are fixed numbers, then

12. Suppose the equation Y=20+10x converts a PSAT math score, X, into an SAT math score, Y. Suppose the average PSAT math score is 48. What is the average SAT math score?

13. Suppose the equation Y = 20 + 10X converts a PSAT math score, X, into an SAT math score, Y. Suppose the standard deviation for the PSAT math score is 1.5 points. What is the standard deviation for the SAT math score?

14. The length in inches of a cricket chosen at random from a field is a random variable X with mean 1.2 inches and standard deviation 0.25 inches. Find the mean and standard deviation of the length Y of a randomly chosen cricket from the field in centimeters. There are 2.54 cm in an inch.