My Math Forum Joint probability density function, probability

 April 26th, 2012, 02:09 AM #1 Newbie   Joined: May 2011 Posts: 28 Thanks: 0 Joint probability density function, probability Hello could you help me with this problem? $\text{Two components have their service life described by joint probability density function:} \\ f_{X,Y}(x,y)= \begin{cases} \frac{1}{2}e^{-x-\frac{y}{2}} &for\; x=>0, y=>0\\ 0=&otherwise \end{cases} \\ \text{What is the probability that second component will live longer?}=$ thanks
 April 26th, 2012, 04:50 AM #2 Newbie   Joined: Feb 2012 Posts: 7 Thanks: 0 Re: Joint probability density function, probability I'm quite possibly wrong about this, and here I'm presuming "Y" is the second component, but you're looking for the probability Pr(Y>X), which is computed through double integrals. $\int_{0}^{\infty} \int_{x}^{\infty} \frac{1}{2} e^{-x-\frac{y}{2}} \quad dy dx$ Which, when evaluated, will give $\frac{2}{3}$ Once again, this is my best guess, not 100% sure!
 April 26th, 2012, 03:28 PM #3 Newbie   Joined: May 2011 Posts: 28 Thanks: 0 Re: Joint probability density function, probability I thought of this firstly and wasn't sure about that (i am not sure about any solution i considered). But seems it could be OK. Could someone else confirm it too?

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