STAT 431 — Applied Bayesian Analysis Homework 2 solution

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1. Of the 70 respondents to the survey after the first lecture, 6 reported having played the card
game Euchre. Assume the survey was a random sample from a large population of “people
like us.”

Suppose we are interested in the proportion π of “people like us” who have played
Euchre. Answer parts (a), (b), (c), and (d) under each of the following priors on π:
(I) a uniform (“flat”) prior

(II) a (very informative) beta prior with parameters α = 100 and β = 100 (see Cowles
Table A.2)

(a) [4 pts] Find a (full) formula for the posterior density function for π. Also, accurately
graph the posterior density function.

(b) [4 pts] Compute the posterior mean and posterior standard deviation of π.
(c) [2 pts] Compute a 95% equal-tailed credible interval for π.

(d) [2 pts] Compute the posterior probabilities of H0 : π ≥ 0.2 and H1 : π < 0.2

2. [3 pts] Cowles, Problem 5.3 [ Note: “(5.2)” refers to equation (5.2) on p. 74. The equation
that precedes it (the transformation-of-variables formula) should have g
−1
in place of g. ]