So I'm working through some computational stats stuff from a free pdf of a book. Specifically I'm looking at their take on the classic Buffon's needle problem. The question has a theoretical part and a computational part. My theoretical background isn't very strong, so I did some research to get those questions answered for me, so I can better understand the computational problem. And the theory seems fairly straight forward on explanation.
My issue is the precursor question to the actual computation problem. The question is this: Let T be the number of crossings in n tosses of the needle, then E=Td/(nl)is an unbiased estimator of 2/π. Calculate the variance of E and thus suggest the best needle length l to use, subject to the restriction l ≤ d.
How would I calculate this? And the best l is simply going to be the one that minimizes the variance of the estimate, right? I understand the definition of variance, but I have no idea how to apply them here.