1. Let X be random variable with density p(x) = x/2 for 0 < x<...

1. Let X be random variable with density p(x) = x/2 for 0 < x < 2 and 0 otherwise. Let Y = X^2−2.

a) Compute the CDF and pdf of Y.

b) Compute P(Y >0 | X ≤ 1.8).

Solutions

Expert Solution

We are given the pdf of X as:

Thus, the CDF of X is given by:

Now. before finding the CDF and PDF of Y, we find its support. Note that the support of X is given by:

0 < X < 2

=> 0 < X² < 4

=> 0-2 < X² - 2 < 4-2

=> -2 < X² - 2 < 2

=> -2 < Y < 2 ; which is the support of Y.

Now, we find the CDF of Y:

Thus, the PDF of Y is given by:

The required probability is given by:

orchestra answered 1 year ago

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