CAS Exam MAS-II Fall 2019, Question 33
Study guide: Exam MAS-II
A coin is tossed 10 times and 7 heads are observed. \theta denotes the unknown probability of heads. You are given the following prior distribution for \theta:
p(\theta) = 2\cos^2(4\pi\theta)where \pi radians = 180°
A Metropolis algorithm with a symmetric proposal distribution is being used to sample from the posterior distribution of \theta. Assume the i^{th} draw from the posterior distribution has resulted in the value of 0.71. The (i+1)^{th} draw is 0.70.
Determine the acceptance probability of the (i+1)^{th} draw.
- A) Less than 0.7
- B) Greater than or equal to 0.7 but less than 0.8
- C) Greater than or equal to 0.8 but less than 0.9
- D) Greater than or equal to 0.9 but less than 1
- E) 1.0
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