For Exercise 20.1, see page 469; for Exercise 20.2, see page 473.
20.3 Expected value. Which of the following is true of the expected value of a random phenomenon?
(a) It must be one of the possible outcomes.
(b) It cannot be one of the possible outcomes, because it is an average.
(c) It can only be computed if the random phenomenon has numerical values.
(d) None of the above is true.
20.4 Expected value. The expected value of a random phenomenon that has numerical outcomes is
(a) the outcome that occurs with the highest probability.
(b) the outcome that occurs more often than not in a large number of trials.
(c) the average of all possible outcomes.
(d) the average of all possible outcomes, each weighted by its probability.
20.5 Expected value. You flip a coin for which the probability of heads is 0.5 and the probability of tails is 0.5. If the coin comes up heads, you win $1. Otherwise, you lose $1. The expected value of your winnings is
(a) $0.
(b) $1.
(c) −$1.
(d) 0.5.
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20.6 The law of large numbers. The law of large numbers says that the mean outcome in many repetitions of a random phenomenon having numerical outcomes
(a) gets close to the expected value as the number of repetitions increases.
(b) goes to zero as the number of repetitions increases because, eventually, positive and negative outcomes balance.
(c) increases steadily as the number of repetitions increases.
(d) must always be a number between 0 and 1.
20.7 The law of large numbers. I simulate a random phenomenon that has numerical outcomes many, many times. If I average together all the outcomes I observe, this average
(a) should be close to the probability of the random phenomenon.
(b) should be close to the expected value of the random phenomenon.
(c) should be close to the sampling distribution of the random phenomenon.
(d) should be close to 0.5.