# Math Help - Poisson distribution sum

1. ## Poisson distribution sum

The question:
Seismic earth tremors occur at an active part of the earth's crust at the average rate of one every two days. What is most likely number of tremors to occur in a week.
My answer: 0.5*7=3.5
Book's answer: 3
What i want to know is the basis upon which the answer was reached?
How do I round of 3.5 in this situations? Normally it rounds to 4, sadly

2. Originally Posted by ssadi
The question:
Seismic earth tremors occur at an active part of the earth's crust at the average rate of one every two days. What is most likely number of tremors to occur in a week.
My answer: 0.5*7=3.5
Book's answer: 3
What i want to know is the basis upon which the answer was reached?
How do I round of 3.5 in this situations? Normally it rounds to 4, sadly
Your answer is the average number of tremors, not the most likely one.

The number of tremors to occur in a week can be approximately considered to be a Poisson random variable (that's in the title of the thread!) with mean $\lambda=3.5$ (using your computation). In other words, the probability of $k$ tremors in a week is about [tex]e^{-\lambda}\frac{\lambda^k}{k!}[/Math]. Compute that value for $k=0,1,2,3,\ldots$ and conclude.

3. Originally Posted by Laurent
Your answer is the average number of tremors, not the most likely one.

The number of tremors to occur in a week can be approximately considered to be a Poisson random variable (that's in the title of the thread!) with mean $\lambda=3.5$ (using your computation). In other words, the probability of $k$ tremors in a week is about $e^{-\lambda}\frac{\lambda^k}{k!}$. Compute that value for $k=0,1,2,3,\ldots$ and conclude.
Okay, but still I would have liked a cut out formula better.