CAS Exam MAS-II Spring 2019, Question 36
Study guide: Exam MAS-II
A farmer with a giant basket of apples and oranges is trying to determine the probability of picking an orange. Consider the following:
- The basket only contains apples and oranges.
- After a piece of fruit is picked from the basket, it is then returned to the basket before another piece is picked.
- The farmer thinks the prior probability of picking an orange follows a beta distribution with probability density function of
p(x) = 12x^2(1-x). - The farmer picks five fruits and one of them is an orange.
- The farmer assumes a Binomial likelihood function to construct a 50% highest posterior density interval (HPDI) using grid approximation with grid points of 0.2, 0.4, 0.5, 0.6, and 0.8.
Determine the lower bound of the farmer's 50% HPDI.
- A) Less than or equal to 0.25
- B) Greater than 0.25 but less than or equal to 0.35
- C) Greater than 0.35 but less than or equal to 0.45
- D) Greater than 0.45 but less than or equal to 0.55
- E) Greater than 0.55
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