Let T be an exponential random variable with parameter lamba.Compute E[T/T<=t]

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- March 19th 2011, 12:44 AMulysses123Exponential random variable
Let T be an exponential random variable with parameter lamba.Compute E[T/T<=t]

- March 19th 2011, 12:51 AMSambit
In case you don't know the general form of computing such an expectation, follow THIS link.

- March 19th 2011, 02:10 AMulysses123
Thanks for the link but I was looking for someone to show me the steps and explain how the expectation is affected because of the conditioning.

- March 19th 2011, 02:21 AMCaptainBlack
- March 19th 2011, 08:48 AMSambit
- March 19th 2011, 06:20 PMulysses123
Thanks for your reply captain black. I thought that P(T/T<=t) will become

P(T) because the fact that the waiting time was <t has no effect on the distribution of the time you will wait due to the memorylessness property, but you have P(T/T<=t)=P(T,T<=t)/P(T<=t) written as P(T)/P(T<t).

I know you are most likely correct, but i would like to understand the logic as i am not getting how you arrived at this. - March 19th 2011, 10:10 PMCaptainBlack