Consider the joint pdf for $X$ and $Y$ given by $f(x,y)=3x, 0 \le y \le x \le 1.$ What is the probability $P(0 \le X\le 0.5, 0.25 \le Y)$?

Asked Sep 08 '13 at 06:03

Active Sep 08 '13 at 06:03

Viewed 47 times

this should be a pretty easy one, but I cannot for the life of me get the supposed answer of $\frac{5}{28}$.

What are my limits of integration supposed to be?

I have tried a million different limits of integration, but the one that seems to make the most sense is:

$\int^\frac{1}{2}_\frac{1}{4} \int^x_\frac{1}{4} 3x \space dy \space dx$.

If someone could just explain to me what the limits of integration are supposed to be and why? Haven't been able to find any examples in my textbooks...

asked Sep 08 '13 at 06:03

JackReacher

2,189

1

Those are the correct limits of integration. – André Nicolas Sep 08 '13 at 06:25
is $\frac{5}{28}$ correct? I've done it a million times and don't get that? – JackReacher Sep 08 '13 at 06:57
2

No, it is way off. – André Nicolas Sep 08 '13 at 07:09

Consider the joint pdf for $X$ and $Y$ given by $f(x,y)=3x, 0 \le y \le x \le 1.$ What is the probability $P(0 \le X\le 0.5, 0.25 \le Y)$?

0 Answers0