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Let $x_1, \ x_2$ be independent random variables.

The probability density function $f(x_i)= 2x \ \ \ \ for \ \ \ \ 0<x_i < 1 $ and $f(x_i)=0 \ \ \ \text{otherwise}$

Then, the density function $f(x_1,x_2)=4x_1x_2$ for $0< x_1, x_2 < 1$

And Y is defined as $Y=X_1+X_2$

What is the distribution function $G(Y)$? Solve by using distribution function method(graph method)

What I did is as follows:

$G(Y)=P(Y \le y)= P( X_1+X_2 \le y)=\int \int f(x_1,x_2) dx_2 dx_1$

And I draw the plot of $Y=X_1+X_2$. But I'm stacking here. Please show me.

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  • $\begingroup$ What are $X_1$ and $X_2$ and how do they differ from $x_1$ and$x_2$? $\endgroup$
    – Dilip Sarwate
    Commented Jan 4, 2016 at 20:56
  • $\begingroup$ There the same. I make a mistake while writing. @DilipSarwate $\endgroup$
    – 1190
    Commented Jan 4, 2016 at 21:12
  • $\begingroup$ A variation of the solution shown at stats.stackexchange.com/questions/48304 will work. $\endgroup$
    – whuber ♦
    Commented Jan 4, 2016 at 23:37

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