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

A random variable X is uniformly distributed between 0 and 1. Two independent observations are made,X1 and X2. Take (X1,X2 ) as a point on the lines X1 +X2 =Y in a cartesian plane. X1 +X2 =Y is triangular.

(a) show that , for 0≤ Y≤ 1, P( X1 +X2 =Y)= ½ Y2

(b) show that , for 1≤ Y≤ 2, P( X1 +X2 =Y)=1- ½ (2-Y)2

2. Relevant equations

f(x)=[tex]\frac{1}{b-a}[/tex] ,for uniform distribution

3. The attempt at a solution

I know that f(x)=1 for 0≤ x≤ 1 since X is uniformly distributed. But how do I solve (a).

Can anyone show me the solution for (a)onlyso that I could solve (b) myself?

Thanks a lot!

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# Homework Help: Cumulative Frequency

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