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exercises_for_prelim

# exercises_for_prelim - 1 Suppose that f(x = sin x for 0...

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1. Suppose that f ( x ) = sin x for 0 x π /2. (a) Sketch this probability density function. (b) Give an acceptance rejection algorithm for generating samples of a random variable with probability density function f . (c) Use your algorithm and the random numbers in Table 1 to generate 4 samples from the probability density function f . (d) On average, how many pairs of random numbers are required to generate a single sample from the probability density function f ? (e) What is the probability that 10 or more pairs of random numbers will be needed to generate a single sample from the probability density function f ? 2. You built a LCG with a period of 2 31 . You have just developed a big simulation in which each replication requires exactly 2 15 random variables. Suppose that you perform 2 40 replications of your simulation experiment, obtaining the outcomes X 1 , X 2 ,..., X n , where n = 2 40 . Is it reasonable to assume that the X i ’s are uncorrelated? Explain. Would your answer be different if

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exercises_for_prelim - 1 Suppose that f(x = sin x for 0...

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