For each of the following de- scriptions of a random variable, indicate whether it can best be modeled by binomial, geometric, Poisson, uniform, exponential, or normal. Answer the associated questions.

(a) Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. What type of random variable is Y? What is P (Y = 3)? What is the expected number of sixes? What is V ar(Y )?

(b) Let U be the random variable that counts the number of accidents that occur at an intersection in one week. What type of random variable is U? Suppose that, on average, 2 accidents occur per week. Find P(U = 2), E(U), and V ar(U).

(c) Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.