So the distribution of
is geometric.
But the distribution of
is not geometric, right?
Mr F says: Correct. The distribution of is not geometric. It has a negative binomial distribution.
I am having trouble determining the distribution of
. My original thought was that it was perhaps the exponential distribution because the exponential distribution can be considered the continuous version of the geometric distribution, and unless I have made an error in my calculations, the Laplace Transform of the exponential dist. is not the same as the solution given in the question.
Mr F says: is clearly a discrete random variable and therefore cannot have a continuous distribution.
Just to double check though, the Laplace transform of a continuous random variable X is
where
is the pdf of
??