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=== Answer 1 === | === Answer 1 === | ||
| − | Hint: You can start with the definition of CDF with respect to Y, i.e, | + | <math>f_{Y}(y)= af_{X}(x)+b</math> |
| − | <math>F_{Y}(y)= P({Y \leq y})</math>. | + | :<span style="color:blue"> 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. </span> |
| + | |||
| + | :<span style="color:blue">Hint:</span> | ||
| + | :: <span style="color:blue">You can start with the definition of CDF with respect to Y, i.e,</span> | ||
| + | ::<math>F_{Y}(y)= P({Y \leq y}) = P({aX+b \leq y})=... </math>. | ||
| + | :: <span style="color:blue">Use derivative to get pdf of Y since you have CDF of Y.</span> | ||
| + | ::<span style="color:blue"> make sure to compare two cases for a>0 and a<0.</span> | ||
| + | :::<span style="color:blue">-TA</span> | ||
=== Answer 2 === | === Answer 2 === | ||
Write it here. | Write it here. | ||
Latest revision as of 19:36, 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
Write it here.
Answer 3
Write it here.
