Question

Write R code that uses the inverse cumulative distribution function method to generate random variables with the following densities from just the uniform distribution on U([0,1]).

(a) f(t) = t³/4 defined on [0,2].

Answer 1

To generate random variables with a given density using the inverse cumulative distribution function method, follow these steps: generate a random variable from the uniform distribution, use the inverse cumulative distribution function to find the corresponding value, and repeat to generate more variables. For the given density f(t) = t³/4, the inverse cumulative distribution function is t = u^(1/3)*2.

Step-by-step explanation:

To generate random variables with the given density function using the inverse cumulative distribution function method, we need to follow these steps:

1. Generate a random variable, u, from the uniform distribution U([0,1]).
2. Use the inverse cumulative distribution function of the given density function to find the corresponding value of t.
3. Repeat steps 1 and 2 to generate more random variables.

For the given density f(t) = t³/4 defined on [0,2], the inverse cumulative distribution function is:
t = u^(1/3)*2