CAS Exam MAS-II Fall 2019, Question 34
Study guide: Exam MAS-II
Assume our data x_1, x_2, \ldots, x_n come from a normal distribution with an unknown mean \mu and known standard deviation, \sigma. We assume a flat prior for \mu.
We use the Metropolis algorithm to sample from the posterior distribution of \mu using a standard normal distribution as a proposal distribution. The chain is allowed to run for 3,000 iterations.
Calculate the probability that the 1000^{th} draw is greater than the 999^{th} draw.
- A) Less than 0.30
- B) Greater than or equal to 0.3 but less than 0.45
- C) Greater than or equal to 0.45 but less than 0.60
- D) Greater than or equal to 0.60 but less than 0.75
- E) Greater than or equal to 0.75
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