Here are the problems written out, in case you don't have the text:

• 3.39: Let X_1, X_2, and X_3 be independent RV's, each with pdf f(x) = e^(-x), 0 < x < infinity, zero elsewhere. Find the distribution of Y = minimum(X_1, X_2, X_3).
  Hint: Pr(Y <= y) = 1 - Pr(Y > y) = 1 - Pr(X_i > y, i = 1,2,3)
• 3.45: Let X have a Poisson distribution with parameter m. If m is an experimental value of a random variable having a gamma distribution with alpha = 2 and beta = 1, compute P(X=0) and P(X=1).
• 3.66: Let the random variable X be N(mu, sigma^2). What would this distribution be if sigma^2 = 0?
  Hint: Look at the mgf of X for sigma^2 > 0 and investigate its limit as sigma^2 -> 0.
• 3.67: Let phi(x) and PHI(x) be the pdf and cdf of a standard normal distribution. Let Y have a truncated distribution with pdf g(y) = phi(y)/[PHI(b) - PHI(a)], a < y < b, zero elsewhere. Show that E[Y] = [phi(a) - phi(b)]/[PHI(b) - PHI(a)].
• 3.70: Let X and Y have a bivariate normal distribution with respective parameters mu_X = 2.8, mu_Y = 110, sigma^2_X = 0.16, sigma^2_Y = 100, and rho = 0.6. Compute:
  (a) Pr(106 < Y < 124)
  (b) Pr(106 < Y < 124 | X = 3.2)
• 4.29: Let X_1 and X_2 be two independent normal RV's, each with mean zero and variance one (possibly resulting from a Box-Muller transformation). Show that:
  Z_1 = mu_1 + sigma_1 * X_1
  Z_2 = mu_2 + rho * sigma_2 * X_1 + sigma_2 * sqrt(1 - rho^2) * X_2
  where sigma_1 > 0, sigma_2 > 0, and 0 < rho < 1, have a bivariate normal distribution with respective parameters mu_1, mu_2, sigma_1^2, sigma_2^2, and rho.
• 4.139: Find the probability that the range of a random sample of size 3 from the uniform distribution over the interval (-5, 5) is less than 7.
• If X_i ~ Bin(n_i, p) for i=1, 2, ..., k, and the X_i's are mutually independent, find the distribution of Y = sum_{i=1}^k X_i.