I am working my way through Feller (3rd ed, vol. 1), and I got stuck on the following problem (IX.9 problem 19a):

A man with n keys wants to open his door and tries the keys independently and at random. Find the mean and variance of the number of trials if unsuccessful keys are not eliminated from further selection. (Assume that only one key fits the door.)

Computing the mean presented no difficultly. I've worked out the variance to be . However, I am not sure how to compute the sum, and would appreciate any hints.

Let X be the random variable number of trials before getting the correct key.

X follows a geometric distribution with p = 1/n.

You'll find the derivations of mean and variance here: http://www.win.tue.nl/~rnunez/2DI30/...tributions.pdf

But personally I think it's easier to calculate and then use the moment generating function.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.