Homework_Assignment_15

Homework_Assignment_15 - Homework Assignment 15: (1) The...

This preview shows page 1. Sign up to view the full content.

Homework Assignment 15: (1) The random variable S follows a binomial distribution with n = 3 and p = 1/3. The following procedure simulates S: Generate a uniform random number U on [0,1] and let 0, if U a S = 1, if a < U b 2, if b < U c 3, if c < U Determine a + b + c . (Ans 2) (2) Mike is practicing his simulation skills. He generates 1000 values of the random variable X as follows: (i) He generates the observed value λ from the gamma distribution with α = 2 and β = 1 (hence with mean 2 and variance 2). (ii) He then generates x from the Poisson distribution with mean . (iii) He repeats the process 999 more times: first generating a value , then generating x from the Poisson distribution with mean . (iv) The repetitions are mutually independent. Calculate the expected number of times that his simulated value of X is 3. (Ans 125) (3) Insurance for a city’s snow removal costs covers four winter months. There is a deductible of 10,000 per month. The insurer assumes that the city’s monthly costs are independent and
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online