CAS Exam MAS-II Fall 2018, Question 27
Study guide: Exam MAS-II
A random variable X is Poisson distributed with mean parameter \lambda.
The posterior distribution of \lambda is:
\lambda = \begin{cases} 0.8; & \mathit{probability} = 0.55 \\ 1.2; & \mathit{probability} = 0.45 \end{cases}A sample of size 10 is drawn from the posterior distribution of \lambda. The 10 sampled values are:
0.8, 0.8, 0.8, 1.2, 0.8, 1.2, 1.2, 0.8, 0.8, 1.2
The 10 sampled \lambda's are stored in a vector named lambdas in R as follows:
lambdas <- c(0.8, 0.8, 0.8, 1.2, 0.8, 1.2, 1.2, 0.8, 0.8, 1.2)
A random sample of size 10 is drawn for the random variable X using the lambdas vector. The R function rpois() is used for sampling in the next line.
rpois(n = 10, lambda = lambdas)
The sampled values of X are:
1, 1, 3, 0, 1, 3, 0, 1, 1, 3
Calculate the posterior predictive probability that X = 1 using the sampling distribution above.
- A) Less than or equal to 0.2
- B) Greater than 0.2, but less than or equal to 0.4
- C) Greater than 0.4, but less than or equal to 0.6
- D) Greater than 0.6, but less than or equal to 0.8
- E) Greater than 0.8
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