Suppose Y is uniform on [0;X + 1], where X is Poisson with mean 3. Find the

probability that Y <= 1.

Can you show all your work? thanks

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- May 28th 2009, 07:17 PMYanFind the probability that Y<= 1?
Suppose Y is uniform on [0;X + 1], where X is Poisson with mean 3. Find the

probability that Y <= 1.

Can you show all your work? thanks - May 29th 2009, 12:18 AMMoo
Hello,

But then, which distribution follows the random variable ? It's a uniform distribution over

Where the pdf is

(because almost surely, we get these boundaries)

Which is

Hence

But the sum is exactly the sum of probabilities of a Poisson distribution with mean 3. So it equals 1.

Therefore,

Looks good to you ?