Probabilty Distribution (Poisson Distribution)

Daniel323

1. The problem statement, all variables and given/known data
It rains on 10.3 days in the town in October on average. Let X denote the number of days in October on which it rains. Assume that rain falling on different days can be treated as independent events. (31 days in October).

Write down an expression for the probability that it rains on a given day in October, and hence state the probability distribution of X.

2. Relevant equations
I've identified the problem to be a Poission Distribution, with Pr(X=x) = [ (λ^x)*(e^-λ) ] / (x!)


3. The attempt at a solution
The probability of it raining on any given day in October = Expected no. of days it will rain / total no. of days = 10.3/31 = 0.332

Hence probability distribution of X would be Pr(x) = [ (0.332^x)*(e^-0.332) ] / (x!)

Sorry this is my first attempt at such a question and am not sure if I have done it right, or if I have even gone about it the right way.

If anyone knows how to tackle this problem, please let me know if I am right or wrong.

Thanks,
Daniel

Daniel323

Anyone have any ideas?