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− | <math>F_{Y}(y)= P({Y \leq y})</math>.We can define an event <math>\left\{ \right.</math> | + | <math>F_{Y}(y)= P({Y \leq y})</math>.We can define an event <math>\left\{ \begin {array} a \\ b \end{array} \right.</math> |
=== Answer 3 === | === Answer 3 === |
Revision as of 19:34, 27 March 2013
Contents
Practice Problem: PDF for a linear function of a random variable
Let X be a continuous random variable with pdf $ f_X(x) $. Let $ Y=aX+b $ for some real valued constants a,b, with $ a\neq 0 $. What is the pdf of the random variable Y?
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
$ f_{Y}(y)= af_{X}(x)+b $
- Unfortunately, this answer is incorrect. Please try again. This problem is important to help you relate CDF to pdf. Please make sure you understand this well.
- Hint:
- You can start with the definition of CDF with respect to Y, i.e,
- $ F_{Y}(y)= P({Y \leq y}) = P({aX+b \leq y})=... $.
- Use derivative to get pdf of Y since you have CDF of Y.
- make sure to compare two cases for a>0 and a<0.
- -TA
Answer 2
$ F_{Y}(y)= P({Y \leq y}) $.We can define an event $ \left\{ \begin {array} a \\ b \end{array} \right. $
Answer 3
Write it here.