1. (a) 0.18, or 18%. Multinomial: 1 and 1 and 1.
(b) Five flips. Geometric, p = 0.2. E(W) = 1/p.
(c) 16/125, or 0.128. Geometric, p = 0.2.
2. 41/e^8. Poisson, lambda = 2 and Lambda = 8. P(S is 0 or 1 or 2).
3. (a) 1/2. First get the density function
by differentiating the cumulative distribution.
(b) 1/20. First calculate E(X^2), which is 3/10.
4. (a) 1/e^2. Exponential with lambda = 2 per day.
(b) 1/e^{17/8}.
(c) It is 1/2 or less.
5. 0.0796. Normal approximation to the binomial distribution. Be sure to use the histogram correction.
6. 0.098. The pill problem.