Math 166-copyright Joe Kahlig, 12C
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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
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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
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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?