Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $f_{X,Y}(x,y) = kxy$, for $0 ≤ x, y ≤ 1,$ otherwise $f_{X,Y}(x,y) = 0$.

(a) Determine $k$ such that $f_{X,Y}(x,y)$ is a PDF.

share|improve this question
2  
Reminder: A property of PDF is such that its integral over its domain equals what. Apply your calculus. I think you know what the what is. –  FrenzY DT. Aug 12 '12 at 12:26

1 Answer 1

up vote 2 down vote accepted

Selected from PDF at WikiPedia.

The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.

As implied, $\int_{R^2} f_{X,Y}(x,y)=1$. (Property of PDF)

Thus $\int_0^1\int_0^1 kxy dxdy=1$, with the rest being mere integration.

share|improve this answer
    
k = 4? :) Thanks so much! –  Fred Aug 12 '12 at 12:37
1  
@Panda Yep, that's the answer. Harder questions involve triangular or circular area of integration which will just complicate integration, though-- e.g. $0<=x<=y<=1$. –  FrenzY DT. Aug 12 '12 at 12:43
    
@Panda Welcome, everyboy gets to learn. –  FrenzY DT. Aug 12 '12 at 23:49

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.