rng_330_3 - Generating Random Numbers: Some Examples...

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Unformatted text preview: Generating Random Numbers: Some Examples Example 1: The following 10 numbers are realizations from a Standard Uniform distribution: .54463 .15389 .85961 .61149 .05219 .41417 .28357 .17783 .40950 .82995 Explain how to use these numbers to generate 10 iid Bernoulli random numbers with a success probability p = . 4. Generate a sample of size 10 from that distribution. Solution: Let Y i = ( 1 if 0 < U i ≤ . 4 , 0 if . 4 < U i < 1 , for i = 1 ,..., 10. Thus by inverse cdf method Y 1 ,...,Y 10 are iid Bernoulli ( . 4) Here the sample generated is 0 , 1 , , , 1 , , 1 , 1 , , Example 2: Generate a random sample of size 10 from the Bin ( n = 10 ,p = . 4) using the above values from U (0 , 1) Solution: X ∼ Bin ( n,p ) means that X is the number of successes in n iid Bernoulli trials with a success probability p . Thus X = Y 1 + Y 2 ,... + Y n where Y 1 ,...,Y n are iid Bernoulli ( p ). In Problem 1, we generated Y 1 ,...,Y 10 ∼ iid Bernoulli ( . 4). Thus set X = Y 1 + Y 2 ,... + Y 10 to obtain...
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

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rng_330_3 - Generating Random Numbers: Some Examples...

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