Random Number and Variate Generation. a. Suppose 0.00000001is a U(0, 1) observat

Question

Random Number and Variate Generation. a. Suppose 0.00000001is a U(0, 1) observation generated by the Crystal Ball random number generator. Convert it to the integer generated by the recursive formula used in the Crystal random number generator, and then generate the next Crystal Ball integer value and U(0, 1) observation. Note- If needed round non integer values down. b. Develop an inverse transform algorithm to generate an observation from the random variable with the following probability distribution function. Generate observations for U = 0.25 and U = 0.5. f(x) = {x/2 for 0 lessthanorequalto x lessthanorequalto 2 0 otherwise c. If U= 0.25 and U= 0.8 are two independent random numbers use them to generate two observations from a normal distribution with mean = 10, and standard deviation = 5.

Explanation / Answer

(c)

You can make use of these two 'U' values as the z-scores and find the corresponding observations.

Data given:

Mean, m = 10

Standard deviation, S = 5

At z = 0.25, we have:

z = (X-m)/S

Putting values:

0.25 = (X-10)/5

Solving we get:

X = 12.5

At z = 0.80, we have:

z = (X-m)/S

Putting values:

0.8 = (X-10)/5

Solving we get:

X = 14

Thus the two observations are 12.5 and 14

Hope this helps !

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