Plot the cdfs of the following distributions. Write an algorithm involving the function random () to generate values from each distribution. In each case, what value is generated if random () returns...

Plot the cdfs of the following distributions. Write an algorithm involving the function random () to generate values from each distribution. In each case, what value is generated if random () returns the values 0.1, 0.5 and 0.9?

(a) The uniform distribution on the interval [α, β]

Use α = 0 and β = 4.

(b) The Weibull distribution with scale parameter α > 0 and shape parameter β > 0 (when α = 1 this is the exponential distribution)

Use α = 1/2 and 2, and β = 1.

(c) A discrete distribution

(d) The Bernoulli distribution with success probability 0

Use γ = 1/4.

(e) The geometric distribution with success probability 0

The floor function means “the largest integer in a” (in other words round down). Use γ = 1/4. (Hint: Begin by writing an expression for Pr{X = a] for the geometric distribution.)