2 votes

Why do we use a Poisson distribution here rather than Binomial?

Let's do the calculation both ways and see what happens: Under a binomial model, we have $n = 80000$, and under the assumption that any individual has an equal probability of being born on any one of $...
heropup's user avatar
  • 136k
1 vote
Accepted

UMVUE of $\mathbb{E}[X^2]=\lambda^2 + \lambda$ where $X\sim\mathrm{Pois}(\lambda)$.

To calculate the value of $$\textrm{E}\left[X_{i}X_{j}\mid\sum_{i=1}^{n}X_{i}=t\right],$$ first note that $$X_{1},X_{2},\ldots,X_{n}\mid\sum_{i=1}^{n}X_{i}=t{\displaystyle \sim\textrm{Multinomial}\...
AOS's user avatar
  • 46
1 vote
Accepted

Finding the limiting distribution of $T_{n}/S_{n}$ as n tends to infinity

First note that $S_{n}$ is the sum of $n^{2}$ many iid $Poi(\lambda/n)$ variates and hence has $Poi(n\lambda)$ distribution. Now see that by Chebycheff's inequality, $$P(|\frac{S_{n}}{\lambda n}-1|\...
Mr.Gandalf Sauron's user avatar
1 vote
Accepted

Expected number of passengers in a bus, if both bus and passengers arrival time have a Poisson distribution.

This solution is incorrect, because this statement is wrong: I've also worked out that the expected length of interarrival interval is 5 minutes. If you choose random interarrival intervals and take ...
Noble Mushtak's user avatar

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