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