(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X,Y,Z random variables.

Let Y and Z be two independent continuous random variables with

common probability density function

f(x) =2exp(-2x); x > 0

0; x < 0

(i) Specify the joint probability density function of (Y;Z).

(ii) Fix x > 0. Let

h(y; z) =

1; y + z 6[tex]\leq[/tex] x

0; y + z > x

Calculate E(h(Y,Z)).

2. Relevant equations

3. The attempt at a solution

i) I don't really understand part i. I think x is a kind of dummy variable but I'm not sure. If it is:

f(y,z)= (2exp(-2y))(2exp(-2z)) = 4exp(-2{y+z}) for y and z [tex]\geq[/tex] 0, and 0 otherwise.

Then E(h(Y,Z)) = the double integral from 0 to infinity both times of h(y,z) * 4exp(-2{y+z}) dy dz

But I'm not totally sure about these limits, or how to sub in h?

Sorry this is very badly typed in and very muddled. Here is the question paper (q8) if this is more helpful. http://www.maths.ox.ac.uk/system/files/private/active/0/paperC2009.pdf [Broken]

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# Homework Help: Joint probability density

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