FIND P(X+Y<=t)
for X~Uniform, Y~Exponential, t>0
GIVEN PDFs
f(x)={1, 0<=x<=1
{0, o.w
f(x)={e^(-x), x>=0
{0, o.w
So this is what I have gotten, but I am unsure of my bounds or if the sums need to be involved (E=Sigma)
Pr(X+Y<=t)=
=E (n=0..t)Pr(X<=n, Y<=t-n)
=E (n=0..t)Pr(X<=n)Pr(Y<=t-n)
=...?
=Int(-inft..t-n)Int(0..1)1*e^(-y)dxdy
=Int(-inft..t-n) [Int(0..1)1dx] e^(-y)dy
=Int(-inft..t-n) [x|0..1] e^(-y)dy
=Int(-inft..t-n) e^(-y)dy
=-e^(-y)|-inft..(t-n)
=-e^(n-t)
i'm pretty sure there are some mistakes in there...
can someone please help????
also, how do you put the math code in?
is it like typing latex?