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
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 ?