Let X be an exponentially distributed stocastic variable with probability density:
f(x;b) = (1/b)e^(-1/b), for x larger than or equal to 0, else 0)
How can I find the cummulative distribution function F(x)?
Thanks!
Haha, well I do know the square root of 36.
The anti-derivative of e^kx is (1/k)e^kx. So the antiderivative when k = -1/b should be -b*e^(-x/b). Multiplying with 1/b negates the b and I'm left with just:
-e^(-x/b)
All right, for some reason I got the antiderivative wrong the last time, which made evaluating the intergral alot harder than it should have been... so proceeding to evaluate:
(-e^(-x/b)) - (-e^(0/b) = (-e^(-x/b)) + 1 = 1 - e^(-x/b)
Is this correct?