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# Probability density function of poission process

Maths and statistics discussion, revision, exam and homework help.

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1. Probability density function of poission process
Question 7 in the image, I don't know where to start

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2. Re: Probability density function of poission process
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.
3. Re: Probability density function of poission process
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!)
4. Re: Probability density function of poission process
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?
5. Re: Probability density function of poission process
Would it be 0?
6. Re: Probability density function of poission process
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?
7. Re: Probability density function of poission process
1/e^ut ?
8. Re: Probability density function of poission process
It clicked and it makes sense now, all cool.

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