Problem 5E

Let X1,X2, . . . ,Xn be a random sample from a gamma distribution with α = 1, θ. Let h(θ) ∝ 1/θ, 0 <θ < ∞, be an improper noninformative prior.

(a) Find the posterior pdf of θ.

(b) Change variables by letting z = 1/θ, and show that the posterior distribution of Z is .

(c) Use 2yz to obtain a (1 − α) probability interval for z and, of course, for θ.

STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0. Probability of success is represented by a p. For a Bernoulli random variable. o X ~ Bernoulli (p) o The expectation of a Bernoulli distribution = the probability of success. (E[X]=p) o Variance [X] = p (1-p) o SD [X] = the square root of the variance Categorical nominal: o You can put the number of successes and failures into a bar plot. BINOMIAL DISTRIBUTION 0 1 When