The random variable X has the PDF fx(x) = { cx-2, if 1 ::;

Chapter , Problem 19

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QUESTION:

The random variable X has the PDF fx(x) = { cx-2, if 1 ::; ::; 2, 0, otherwIse. (a) Determine the value of c. (b) Let A be the event {X > 1.5}. Calculate P(A) and the conditional PDF of X given that A has occurred. (c) Let Y = X 2 . Calculate the conditional expectation and the conditional variance of Y given A.

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QUESTION:

The random variable X has the PDF fx(x) = { cx-2, if 1 ::; ::; 2, 0, otherwIse. (a) Determine the value of c. (b) Let A be the event {X > 1.5}. Calculate P(A) and the conditional PDF of X given that A has occurred. (c) Let Y = X 2 . Calculate the conditional expectation and the conditional variance of Y given A.

ANSWER:

Step 1 of 3

Given:

The variable X has the PDF,

(a) Let . Calculate the conditional expectation and the conditional variance of Y given A.

For the defined PDF,

Thus, the required PDF for X is,

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