The discussion focuses on generating a random variable with the distribution function F(x) = 1/2(x + x²) for 0 < x < 1. The proposed method involves using a uniformly distributed random variable U over the interval (0,1) and setting U equal to 1/2(x + x²). The transformation leads to the equation 2U = x + x², which is a critical step in deriving the random variable. Participants confirm that this approach aligns with standard methods found in course materials and textbooks.
PREREQUISITESStudents in statistics or probability courses, data scientists, and anyone interested in random variable generation techniques.
twoski said:Homework Statement
Give a method for generating a random variable with distribution function
F(x) = 1/2[itex](x+x^{2})[/itex]
0<x<1
The Attempt at a Solution
From what i can tell i am supposed to do something like:
Let U be a uniformly distributed random variable over (0,1).
U = 1/2[itex](x+x^{2})[/itex]
2U = [itex]x+x^{2}[/itex]
Am i on the right track?