| Line 19: | Line 19: | ||
=== Answer 1 === | === Answer 1 === | ||
| − | Hint: You can start with the definition of CDF with respect to Y, i.e, | + | Hint: |
| − | <math>F_{Y}(y)= P({Y \leq y})</math>. | + | : You can start with the definition of CDF with respect to Y, i.e, |
| + | :<math>F_{Y}(y)= P({Y \leq y}) = P({aX+b \leq y})=... </math>. | ||
| + | : 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 === | === Answer 2 === | ||
Write it here. | Write it here. | ||
Revision as of 12:22, 26 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
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
Write it here.
Answer 3
Write it here.
