3.5 You are to pay $1 to play a game that consists of drawing one ticket at random from a box of numbered tickets. You win the amount (in dollars) of the number on the ticket you draw. The following two boxes of numbered tickets are available.a Find the expected value and variance of your net gain per play with box I.b Repeat part (a) for box II.c Given that you have decided to play, which box would you choose and why?

3.5P You are to pay $1 to play a game consisting of drawing one ticket at random from a box of numbered tickets. You win the amount (in dollars) of the number on the ticket you draw. Two boxes are available with numbered tickets as shown below: 0, 1, 2 0, 0, 0, 1, 4 3.6P The graph in Figure 3.11 shows the age distribution for AIDS deaths in the United States through 1995. Approximate the mean and standard deviation of this age distribution. How does the mean age compare to the approximate median age? Distribution of AIDS Deaths, by Age: 1982 Through 1995 305,843 Deaths Under 12 years 60 years and over 1% 4% 50-59 years 13-29 years 8% 18% 40-49 years 25% 30-39 years 45%