In Example 2c we simulated the absolute value of a unit normal by using the rejection procedure on exponential random variables with rate 1. This raises the question of whether we could obtain a more efficient algorithm by using a different exponential density—that is, we could use the density g(x) = λe−λx. Show that the mean number of iterations needed in the rejection scheme is minimized when λ = 1.
Answer to relevant QuestionsIn Problem 21, how many different paths are there from A to B that go through the point circled in the following lattice? Problem 21 Consider the grid of points shown at the top of the next column. Suppose that, starting at ...From a group of n people, suppose that we want to choose a committee of k, k ≤ n, one of whom is to be designated as chairperson. (a) By focusing first on the choice of the committee and then on the choice of the chair, ...In how many ways can n identical balls be distributed into r urns so that the ith urn contains at least mi balls, for each i = 1, . . ., r? Assume that Use the rejection method with g(x) = 1, 0 < x < 1, to determine an algorithm for simulating a random variable having density function Use the inverse transformation method to present an approach for generating a random variable from the Weibull distribution
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