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?