[mcp2]

Question 7 in the image, I don't know where to start

[Zhen Lin]

It's asking you to show that the time between events in a Poisson process is an exponential r.v. Have you never seen this before? Use the hint to get the complementary c.d.f. of T, subtract that from 1 to get the c.d.f., and differentiate to get the p.d.f.

[mcp2]

Still don't understand :/ I'm trying to use the normal Poisson forumla with ut as the mean so it comes out as (e^-ut)(ut/t!)

[Zhen Lin]

I don't know how you could be getting t! from anywhere. t is a real number — do you know what, say, is? Try again — in the time period [0, t], what is the probability of 0 events?

[mcp2]

Would it be 0?

[Zhen Lin]

No...? The number of events in the interval [0, t] is a Poisson r.v. with mean , like the question says. So what's the probability of 0 events?

[mcp2]

1/e^ut ?

[mcp2]

It clicked and it makes sense now, all cool.