A PDF is defined by the function
[Ce^(-t/10), 0 <= t <= infinity]
f(t) ={
[0, elsewhere]
where C is a constant. Find the value of C.
By my reckoning, if f(t) is a PDF, then its area is 1. So the integral from 0 to infinity of Ce^(-t/10) = 1
the antiderivative of Ce^(-t/10) = -10Ce^(-t/10): I'll call this function F(t).
I'm fine up to here, but now to find the area don't I have to let F(infinity)-F(0) = 1, and solve for C? F(0) I can do, but F(infinity)?
My first thought was that although the domain says 0 <= t <= infinity, it's really the values for which the function is positive. So I was going to let the original function f(t) = 0 and find the x-intercept in terms of C, and that would replace the infinity in the domain, but I can't rearrange Ce^(-t/10) = 0 to make t the subject.
I'm really stuck with this, anyone have any ideas?