91Ó°ÊÓ

Classify each random variable as either discrete or continuous. a. The number of boys in a randomly selected three-child family. b. The temperature of a cup of coffee served at a restaurant. c. The number of no-shows for every 100 reservations made with a commercial airline. d. The number of vehicles owned by a randomly selected household. e. The average amount spent on electricity each July by a randomly selected household in a certain state.

A roulette wheel has 38 slots. Thirty-six slots are numbered from 1 to \(36 ;\) half of them are red and half are black. The remaining two slots are numbered 0 and 00 and are green. In a \(\$ 1\) bet on red, the bettor pays \(\$ 1\) to play. If the ball lands in a red slot, he receives back the dollar he bet plus an additional dollar. If the ball does not land on red he loses his dollar. Let \(X\) denote the net gain to the bettor on one play of the game. a. Construct the probability distribution of \(X\). b. Compute the expected value \(E(X)\) of \(X\), and interpret its meaning in the context of the problem. c. Compute the standard deviation of \(X\).

A roulette wheel has 38 slots. Thirty-six slots are numbered from 1 to \(36 ;\) the remaining two slots are numbered 0 and 00 . Suppose the "number" 00 is considered not to be even, but the number 0 is still even. In a \(\$ 1\) bet on even, the bettor pays \(\$ 1\) to play. If the ball lands in an even numbered slot, he receives back the dollar he bet plus an additional dollar. If the ball does not land on an even numbered slot, he loses his dollar. Let \(X\) denote the net gain to the bettor on one play of the game. a. Construct the probability distribution of \(X\). b. Compute the expected value \(E(x)\) of \(X,\) and explain why this game is not offered in a casino (where 0 is not considered even). c. Compute the standard deviation of \(X\).

A fair coin is tossed repeatedly until either it lands heads or a total of five tosses have been made, whichever comes first. Let \(X\) denote the number of tosses made. a. Construct the probability distribution for \(X\). b. Compute the mean \(\mu\) of \(X\). c. Compute the standard deviation \(\sigma\) of \(X\).