Using this generator get a weibull variate for α=8, β=0.75, v=0, and R = 0.612.

Weibull Distribution

$f(x)=\frac{\beta}{\alpha}\left(\frac{x-v}{\alpha}\right)^{\beta-1} e^{-\left(\frac{x-v}{\alpha}\right)^{\beta}}; x \ge v$

Algorithm:

Step 1: Compute c.d.f. for given random variable X for uniform or Rectangular Distribution it is given by

$f(x)=1-e^{-\left(\frac{x-1}{a}\right)^{\beta}}$

Step 2: Set $f(x) = R $ where R represents a random number uniformly Distributed over [0,1]

$\therefore R=1-e^{-\left(\frac{x-V}{\alpha}\right)^{\beta}}$

*Step 3: * Solve …