Assume we have a random number generator that can generate a random number uniformly distributed in the range $[0, 1]$. If now we want to use this generator to generate a random number X that has a negative exponential distribution $f_X(x) = ae^{−bx} (x ≥ 0)$, where $a, b \geq 0$.
Suppose the random number generator generates $0.8$. What should be the value for X?
I am totally confused... I dont get the point of this question. The random number generator $X \sim U[0, 1]$ according to the question. But why $X$ is negative exponential in the following sentences?
Could anyone give some hints about the model of this question? Thanks in advance!
They never say that $X$ is uniform. $X$ is negative exponential. The uniform variable is unnamed.
They want you to describe a way to transform $U[0,1]$ variable into a negative exponential variable, then apply that transformation to $0.8$. Technically, there are many ways of doing this, but I think there is one that stands out as better than most others: just apply the inverse of the cumulative distribution function (for the negative exponential $X$) on $0.8$.