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
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