Homework Help: Questions from a probabilty final

1. Dec 10, 2009

SNOOTCHIEBOOCHEE

1. The problem statement, all variables and given/known data

Few questions here, nothing super tough, just cant get it/ want verification.

1. The following experiment is repeated twice: a fair coin is flipped repeatedly until it lands heads. Let X be the number of flips required in the first trial and Y the number required in the second trail. Find probability that X<Y.

2. Let U be a uniform (0,1) random variable. Find the density of ln(1/U)

2. Relevant equations

3. The attempt at a solution

1. So i figured the way to approach this problem is find P(X=Y) then we would calculate 1-P(X=Y)= P(X>Y or X<Y) then divide that by two to get P(X<Y).

So i wanted to calculate P(X=Y). i wasnt sure how to approach this, so i fixed X at some number k then found the probability that Y=k, which is 1/2^k. Is this right?

cause then the answer we get is 1-(1/2)^k/2. But im not convinced of that answer.

2. This seems like it would be a one to one substitution.

Since U is uniform on (0,1) its density function is just 1.

Y=ln(1/u)
e^-Y= U

dy/du= -1/U

So our formula is 1/|-1/U|= U = e^-Y

This correct?