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

AI Thread Summary
The discussion focuses on calculating the probability P(Y>5) given that X is an exponentially distributed random variable with a rate of 2. The conditional probability P(Y>5|X=x) is defined as e^(-3x). The solution involves integrating this conditional probability over the distribution of X. The final answer is confirmed to be 2/5, although the original poster initially struggled with the calculation. Ultimately, they resolved their confusion regarding the solution process.
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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:
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nvm i figured it out
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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