# Probability and convolution

1. Apr 7, 2006

### barneygumble742

hi,

i'm given the density function
fx(t) = 0 (t<0)
fx(t) = 2t (0<t<1)
fx(t) = 0 (t>1)

how can i solve this using the fundamental theorem of calculus?

i had a similar situation before where my function was:
fx(t) = 0 (t<0)
fx(t) = 1 (0<t<1)
fx(t) = 0 (t>1)

and the g(t) i came to was:
g(t) = 0
g(t) = t
g(t) = 2-t
g(t) = 0

some work from the previous situation:
integral of fx(u) * f(t-u) du
integral of 0 for t<0 = 0
integral of 1 for 0<t<1 = t
integral of 1 for 0<t-t<1 = 2-t for 1<t<2
integral of 0 for t>2 = 0

finding the probability between alpha and beta:

integral of g(t) dt from 0.45 to 1.35 = integal of t dt from 0.45 to 1 + integral of 1 to 1.35 = 0.6875

i tried to apply the same principles where fx(t) = 2t but i keep getting the wrong answer.
for my simulation, x1 = rnd (a random number between 0 and 1) and x2 = sqrt(rnd) (square root of another random number). i added the numbers and i'm finding the expected value and variance perfectly and my theory supports it. however i'm not getting the theory for my probability of being between alpha and beta.

i think i'm loosin' it!