Question

A uniform random variate is required to lie on interval (5/8; 1). Acceptance-rejection technique is used to generate such random variates. How many random numbers have to be generated in order to produce 2000 random variates? (Do not generate any random numbers.).

Hint: Think of the random variate generation process as resulting in rejections until the random variate satisfies the desired conditions, resulting in the 1^st acceptance.                                        [5]

Answer 1

The probability of acceptance for the random variant is 1-5/8 = 3/8.

Now if we want to generate 2000 random variants. Then we know that each random number has a 3/8 probability of acceptance. Thus if we generate n random numbers then 3n/8 numbers on average will belong to the random variates.

Here the number random variants = 2000 i.e.

. Thus on average, we should generate 5333.33 random numbers which can be approximated to 5334 random numbers.