Recent content by Aaron10

I looked at this again, and think if I set it up so that if Pr(Y>a+b|Y>a) = Pr(Y>b), then Y is memoryless. I would then have Pr(Y>a+b)/Pr(Y>a) = Pr(Y>b). I solved this using (∫λe^(-λx)dx from (a+b) to ∞)/(∫λe^(-λx)dx from (a) to ∞). This equals e^(-λb) which is equal to Pr(Y>b). Thus, Y is...

Homework Statement Let X be an exponential random variable with rate parameter λ>0. Let [x] denote the smallest integer greater than or equal to x (called the ceiling function). For example, [0.12]=1 and [2]=2. Let Y=[X]. a) Find the pmf of Y=[X] b) Does Y have the memoryless property...

That's correct, sorry, typo on my part. It's actually where to go from there that confuses me. I know the ∫0 to ∞((e^tw)f(w)dw gives me Mw(t), so I think ∫0 to ∞ ((w^k)f(w))dw should give me E(W^k), but I don't know how to actually find this or if it is the best way to approach it. Also...

Homework Statement X is distributed exponentially with λa=2. Y is distributed exponentially with λb = 3. X and Y are independent. Let W=max(X,Y), the time until both persons catch their first fish. Let k be a positive integer. Find E(W^k). Also, find P{(1/3)<X/(X+Y)<(1/2)}...