Use the following result: if and are two independent random variables which have a density, namely for and for , then has a density , which is given by .
Let X and Y be independent exponential random variables with and
Find the joint probability distribution .
I know that the probability density function for X is for x>0 and 0 otherwise.
I know that the probability density function for Y is for x>0 and 0 otherwise.
I am not sure about jointly. Do I simply multiply them together?
I have no idea how to begin this part, although I know the answer is .04.
Can anyone help?
...where is the so called 'Heaviside step function' ...
Now if we set the p.d.f. of Z is given by the convolution of and ...
Using a basic property of the Laplace Transform we have that...
... so that...
... and from (8) taking the inverse Laplace Tranform...
Once You have the p.d.f. of Z You can obtain the requested probability by integration...