Thread: approximations for discrete distributions

The number of trees in one acre has a Poisson distribution with mean 60. Assuming independence, compute approximately , where X is the number of trees in 100 acres.

Could someone work this problem out for me or a similar one? I have a few of this type to do. Thank you

The sum of n independent Poisson random variables each with parameter is itself a Poisson random variable with parameter .

So X is Poisson random variable with parameter 60*n = 60*100 = 6000. Therefore, X has a mean a 6000 and a variance of 6000.

Since n is fairly large, is approximately by the central limit theorem

so find

If you were dealing with a strict inequality, the answer would be different.