What is the Probability of Y being Greater than 5 Given X Equals a Constant?

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SUMMARY

The probability of Y being greater than 5 given that X equals a constant is computed using the joint distribution of the random variables X and Y. In this case, X follows an Exponential distribution with a rate parameter of 2, denoted as X~Exponential(2). The conditional probability P(Y>5|X=x) is defined as e^(-3x). The final computed probability p(Y>5) is definitively 2/5, as confirmed by the professor's solution.

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Homework Statement



Let X and Y be jointly absolutely continuous Random Variables. Suppose X~Exponential(2) and that P(Y>5|X=x)=e-3x. Compute p(Y>5).

Homework Equations



X~Exponential(2) means that its a exponential distribution integrated from -inf to inf, then sub lambda as 2.

The Attempt at a Solution

the answer is 2/5 which is given but i don't get that... here is my prof's solution somehow he got 2/5
http://i.imgur.com/PCgDI.jpg

I don't understand how to get it, i end up getting infinity in the last step
 
Last edited:
Physics news on Phys.org
nvm i figured it out
 

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