Sum of Random variable densities: f(x) =1, if 0<x<1 and f(x)=0, otherwise

Hello all

Please help me with the below question
If X and Y are independent random variables each with density function f given by f(x) =1, if 0<x<1 and f(x)=0, otherwise. Then determine the density function of X+Y.

Thanks in advance

mathdaemon said:

Hello all

Please help me with the below question
If X and Y are independent random variables each with density function f given by f(x) =1, if 0<x<1 and f(x)=0, otherwise. Then determine the density function of X+Y.

Thanks in advance

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What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Note that the sum of independent random variables may be defined as the convolution of the two, see for example
"The probability density function of the sum of two independent random variables U and V, each of which has a probability density function, is the convolution of their separate density functions: ..."
https://en.wikipedia.org/wiki/Probability_density_function#Sums_of_independent_random_variables
or as the mixture distribution, for example see
https://en.wikipedia.org/wiki/Mixture_distribution

It appears to me that you are using the convolution, but could you please confirm?

Frankly, I had no idea what to look for, so I just posted the question without trying out anything. You gave me the direction and I reached the destination. Thanks a lot.