Trouble with Convolution of Random Variables [closed]

probability probability-theory probability-distributions

Solution 1:

The joint support $(D,C)$ is a parallelogram with vertices

$(0,0);(1,1);(1,2);(0,1)$

Thus when $C\in(0;1)$ the integral is

$$f_C(c)=\int_0^c f_{CD}(c,d) d d$$

Thus when $C\in[1;2)$ the integral is

$$f_C(c)=\int_{c-1}^1 f_{CD}(c,d) d d$$

$d$ is an ugly letter for a rv...this confuses with the differential

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