hello all(adsbygoogle = window.adsbygoogle || []).push({});

I have been workin on some problems involving conditional probability and continuous random variables and the thing is i dont know if i get the limits correct, anyway here is the problem, check it out, any suggestions would be helpful

[tex]f(y_1,y_2) =\left\{\begin{array}{cc}2,&\mbox{ if }

0\le y_1\le 1, 0\le y_2\le 1, y_1+y_2\le 1\\0, & \mbox{elsewhere}\end{array}\right[/tex]

what i want to find was

[tex]P(Y_1\ge \frac{1}{2}|Y_2\le \frac{1}{4})[/tex]

[tex]=\frac{\int_{0}^{\frac{1}{4}} \int_{\frac{1}{2}}^{1-y_2} 2 dy_1 dy_2}{\int_{0}^{\frac{1}{4}} \int_{0}^{1-y_2} 2 dy_1 dy_2}=\frac{3}{7}[/tex]

also I wanted to find

[tex]P(Y_1\ge \frac{1}{2}|Y_2=\frac{1}{4})[/tex]

[tex]=\frac{\int_{\frac{1}{2}}^{\frac{3}{4}} 2 dy_1}{\int_{0}^{1} 2 dy_1}=\frac{1}{4}[/tex]

about the 3/4 that is where the intersection occurs

now have i got my limits correct? how do i know if i have the limits correct? are my answers corrrect?

steven

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Conditional Prob -cont random variable

**Physics Forums | Science Articles, Homework Help, Discussion**