couple of probability questions

[trickslapper]

Suppose that X is a random variable whose range is the set of positive integers. Let Y=X/(X+1)

a. what is the range of Y
b. determine the PMF of Y
c. Repeat parts (a) and (b) for the random variable Z = (X+1)/X


Let X denote the number of trials until the third success in a sequence of Bernoulli trials with success probability p.

a. Express the proportions of failures, Y, in terms of the random variable X.
b. Obtain the PDF of the random variable Y in part (a).


Not really sure how to approach these, any ideas?

 

[tkhunny]

a: 1/2, 2/3, 3/4, 4/5, 5/6, etc. A discrete distribution on [½,1).
b: can we do that without the PMF of X?

Now what?