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Let's say we have a pseudo-random number U = 0.334. I want to use this U...

Let's say we have a pseudo-random number U = 0.334. I want to use this U to generate an Exponential (λ = 1/4) random variate. How do I do this?  

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Answer #1

cdf of Exponential Distribution with = 1/3 is given by:

F(x) = 1- e-x/4--------------(1)

This is equated to the Random Number generated = 0.334and solved for x.

Equating (1) to 0.334, we get:

1- e-x/4 =0.334

i.e.,

e-x/4  =0.666

i.e.,

-x/4 = -0.4045

So,

x = 0.4045 x 4 = 1.618

So,

answer is:

1.618

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