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Math 166-copyright Joe Kahlig, 12C Page 1 Section 3.2: Measures of Central Tendency ( Part 1) Example: A game cost $2 to play. The game consists of rolling two fair die. If you get a sum of 2 or 3, then you win $50. A sum of 4 wins $10. Every other sum constitutes a loss of the game. Let X be the player’s net winnings. A) Find the probability distribution of X. B) Would you rather play this game or run the game? C) If this game is played 1 million times, what results would be expected? Definition: The expected value or mean of a discrete random variable X, denoted E(X) is Note: A game is said to be fair when Math 166-copyright Joe Kahlig, 12C Page 2 Example: A carnival has a game where the player draws two different card from a standard deck of cards. If both cards are diamonds, then the player wins $5. One diamond drawn means the player wins $1. What should be charged in order to make the game fair? (or as fair as possible.) Example: A company sell one year term life insurance policies for $800. The face value of the policy is $25,000. Life insurance tables have determined that the probability that a person interested in this pollicy will survive the year is 0.97. What is the companies expected profit on this product? Math 166-copyright Joe Kahlig, 12C Page 3 Example: A multiple choice exam has 10 questions where each question has 5 answers. If a student guesses at all of the questions, what is the expected number of questions that the student will get correct? What is the student’s expected grade on the exam? Note: The expected value of a binomial distribution with n trials and probability of success, p, is Example: A company has a production line that has a historic defect rate of 4.5%. If a random sample of 450 items are collected, how many of the items would we expect to be good?