A radioactive material emits alpha particles at a rate described by the density function
f(t) = .1e^(-.1t)
Find the probability that a particle is emitted in the first 10 seconds, given...
a) NO particle is emitted in the first second
b) NO particle is emitted in the first 5 seconds
c) a particle is emitted in the first 3 seconds
d) a particle is emitted in the first 20 seconds
for C and D, i think i'm supposed to integrate f(t) from 0 to 3 (and 0 to 20), which gives the probability of those events happening. Then to find f(t given the event), would it be f(t) / the probabilities of the above? But then, if a particle is emitted in the first 3 seconds, wouldn't the probability be 1? And I'm not sure how to set up the integral at this point for part D (the 20 seconds), because I'm unsure of the bounds.
I have no idea where to begin with A and B, a little push in the right direction would be great! Thanks