SOLUTION: Given the function f(x)=4x3, Explain how you can generate random numbers from this function using the inverse transform method

Question 1021585: Given the function
f(x)=4x3, Explain how you can generate random numbers from this function using the inverse transform method
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
f(x) = 4x^3
:
rewrite with f(x) = y
:
y = 4x^3
:
compute inverse function by solving for x
:
x^3 = y/4
x = (y/4)^(1/3)
interchange the y's and x's
y = (x/4)^(1/3)
:
f^(-1)(x) = (x/4)^(1/3)
:
Procedure to generate random numbers from f(x) using f^(-1)(x)
:
******************************************************************************
1) Generate a random number u from the standard uniform distribution in the interval [0,1]
2) Compute x = f^(-1)(u)
3) Take x to be the random number drawn from the distribution described by f(x)
*******************************************************************************
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