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Poisson approximation?
I'm doing my math HW and in one question I am asked to:
Let x be a binomial random variable with n=20 and p= .1
Use the Poisson approximation to calculate
P(x≤2).
I have use the formula and try to do it in different ways but I still don't get the answer that my book gives which is .6767
I get .2706 and any other way I do it it gives me a different answer.
So can someone explain to me in a clear way how to do it correctly so that I get .6767
Thanks.
So you add all the values when you find them for 0,1, and 2? My book said none of that and in that case it makes sense. Thanks
4 Answers
- Anonymous1 decade agoFavorite Answer
mean = n * p = 2
var = n * p * q = 1.8
Poisson: e^(-np) * (np)^k / k!
k=0, P(0) = .135
k=1, P(1) = .271
k=2, P(2) = .271
Summation = 0.677
- 1 decade ago
The way you answered it is by finding P(x = 2). The question asks for the cumulative number up to 2. The only way that you can do it by hand is to use calculus, or alternatively you could use a calculator (probably a graphing calc) to find the cumulative probablity, that is, the probability of x being less than or equal to two. To do that, most calculators that have poisson would be to use the poissoncdf
- ?Lv 44 years ago
you could attempt the combinatorial attitude first. Then use your e book's formulation to calculate the approximation, that's clever because of the fact the numeric combinatorial calculation is unwieldy (in spite of the actuality that a working laptop or computing gadget calculator can do it).
