Cumulative Frequency Homework: Solving (a) and (b)

[cyt91]

Homework Statement

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

Homework Equations

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

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) only so that I could solve (b) myself?

Thanks a lot!

 

[LCKurtz]

Homework Statement

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

This is a very confused statement of the problem. First of all, I suppose that last Y2 is supposed to be Y². Use the X² icon for superscripts.

Secondly, you are apparently confused between a random variable Y and its range. Here you are giving Y as the sum of two random variables: Y = X₁ + X₂ (you can use the subscript button too). Per the title of your post, you are apparently seeking the cumulative distribution function for Y. The usual notation is to use lower case for the range values, so you want to calculate P(Y ≤ y) = P(X₁ + X₂ ≤ y), not P( X₁ +X₂ =Y). This is where you have two cases depending on whether y < 1 or y > 1.

Does stating the problem clearly help you any?