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Back to 4.2 Mean or Expected Value and Standard Deviation

4.2 Exercise 4

Avg difficulty 2.5

Suppose you play a game with a biased coin. You play each game by tossing the coin once. P(heads) = 2 3 \frac{2}{3} and P(tails) = 1 3 \frac{1}{3}. If you toss a head, you pay $6. If you toss a tail, you win $10. If you play this game many times, will you come out ahead?

a. Define a random variable X.

b. Complete the following expected value table.

x
WIN 10 13\frac{1}{3}
LOSE –123\frac{–12}{3}

c. What is the expected value, μ? Do you come out ahead?

OpenStax Introductory Statistics 2e, 4.2 Mean or Expected Value and Standard Deviation, exercise 4

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Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.