Solution Found!
The random variable X has the PDF fx(x) = { cx-2, if 1 ::;
Chapter , Problem 19(choose chapter or problem)
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.
Questions & Answers
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,