Pdf of random variable

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Homework Statement


random variable of X has pdf: f(x) = (3/16)*x2 from interval (-2,2). Also, E(X) = 0, and E(X2) = 12/5. Find the pdf of Y = X2


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The Attempt at a Solution


I don't really know where to start.
 

Answers and Replies

  • #2
vela
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There are a couple of methods to do this. One of the easiest to understand conceptually is to calculate the probability that Y is less than or equal to some y in terms of X.

P(Y≤y) = P(X2≤y) = ...

Now P(Y≤y) is just FY(y), the cdf of Y, so to find fY(y), the pdf of Y, just differentiate it.
 
  • #3
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so first I should find the cdf of X by integrating the pdf of X, then I should find the cdf of Y, and then differentiate that to get the pdf of Y? How do I get the cdf of Y from the cdf of X^2?
 
  • #4
vela
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You don't need to find the cdf of X first, though you certainly can use it to solve the problem. I think you should first determine what interval [a,b] of X corresponds to the condition X2≤y. Then you use P(X2≤y) = P(a≤X≤b). This second probability you can calculate using the cdf of X if you found that or you can find it using fX(x), whichever you prefer.
 

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