Suppose that we generate a pseudo-random number U = 0.128. Use this to generate an Exponential (λ = 1 / 3) random variate.

The generated random variate is X = 6.173

Explanation:

To generate an exponential random variate (with parameter λ) from a pseudo-random number U, we use the formula:

X = - ln (U) / λ

Fro the given problem, we have U = 0.128 and λ = 3.

So, X = - In (0.128) / (1/3) = - In (0.128) / 0.333 = 2.056/0.333 = 6.173