- #1

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**can not build up the integral structure**, I intuitively think the result is just 1/mu, but I can not prove it to myself

**could you help me about that and building the integral structure??????**

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- Thread starter mertcan
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- #1

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- #2

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- #3

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hi, I tried to do my work related to E(X1|X1<X2)*P(X1<X2), and X1, X2 are exponential random variables with rate respectively $$\lambda, \mu$$ I found a answer but I think it is wrong so could you tell me which part of my work is wrong??????? ( I also looking forward to your answers @andrewkirk @Ray Vickson :) )

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- #5

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@andrewkirk @Ray Vickson I upload my work 2 ,let me express again that E(X1|X1<X2)*P(X1<X2), and X1, X2 are exponential random variables with rate respectively $$\lambda_1,\lambda_2$$I found a answer but I think it is wrong so could you tell me which part of my work is wrong??????? ( by the way I did my best to make it not dark, when I upload, the top and bottom parts get dark a little )

- #6

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can not build up the integral structure, I intuitively think the result is just 1/mu, but I can not prove it to myselfcould you help me about that and building the integral structure??????

Are X and Y independent? In any case, you first need to find $$\mathbb{E}[X|Y, X>Y]$$. To do this, first write $$\mathbb{E}[X]$$, and then change the lower limit. After finding $$\mathbb{E}[X|Y, X>Y]$$, you will need to average over all values of Y. If you go through these steps, you should be able to find what you want.

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