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Q. 10.11

A First Course in Probability
Found in: Page 431
A First Course in Probability

A First Course in Probability

Book edition 9th
Author(s) Sheldon M. Ross
Pages 432 pages
ISBN 9780321794772

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Short Answer

Use the rejection method with g(x) = 1, 0 < x < 1, to determine an algorithm for simulating a random variable having density function


The algorithm is generateY~g(which is unform) and take random number U(0,1).

See the step by step solution

Step by Step Solution

Step 1: Given Information

We have given the density function


Step 2: Simplify

Finding the upper bound of f on the interval (0 , 1). Using the differentiation, we have


which implies the equality


So, the maximum value of f is assumed to be in point x=35 and it is equal to localid="1648210382401" f352.0736:=c. So, the algorithm is as follows: generate Y~g(which is uniform) and take random number U(0, 1). Consider if


and in that case declare X=Y. Otherwise, go to the step 1 again.

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