So the question states:
"Let X and Y be independent random variables, each exponentially distributed with parameter lambda. Find the density function and the distribution function of X + Y ."
I mostly understand what density and distribution functions are but I never learned how to calculate them from such little information. The only hint that was given said that "the probability density function of the sum of two independent random variables X and Y, with the respective probability density functions fx and fy, is given by the formula: fx+y(t) = integral from -infinity to +infinity of fx(s)*fy(t-s)*ds"
Any ideas would be very appreciated.
"Let X and Y be independent random variables, each exponentially distributed with parameter lambda. Find the density function and the distribution function of X + Y ."
I mostly understand what density and distribution functions are but I never learned how to calculate them from such little information. The only hint that was given said that "the probability density function of the sum of two independent random variables X and Y, with the respective probability density functions fx and fy, is given by the formula: fx+y(t) = integral from -infinity to +infinity of fx(s)*fy(t-s)*ds"
Any ideas would be very appreciated.