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Practice Problem: What is the conditional density function
Let X be a continuous random variable with probability density function
$ f_X(x)=\left\{ \begin{array}{ll} c x^2, & 1<x<5,\\ 0, & \text{ else}. \end{array} \right. $
Let A be the event $ \{ X>3 \} $. Find the conditional probability density function $ f_{X|A}(x|A). $
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
Hint:
- Find c by,
- $ \int_{-\infty}^{\infty} f_{X}(x)dx =1. $
- $ f_{X|A}(x|A)= \frac{f_{X}(x)}{P({X>3})} = \frac{f_{X}(x)}{1- F_{X}(3)} . $ -TA
Answer 2
Write it here.
Answer 3
Write it here.
