Question

Suppose that X is a Poisson random variable with lambda = 9

Approximate the probability that X is less than 6 Without continuity correction

Answer 1

$$ \Large{
P(X=k) = \frac{e^{-\lambda} \cdot \lambda^k }{k!} ~~,~ k=0,1,2,...

\\~\\ P(X\leq 6) = \sum_{k=0}^{6}\frac{e^{-9} \cdot 9^k }{k!}
}
$$

Answer 2

any question so far?

Answer 3

http://www.wolframalpha.com/input/?i=Sum%28exp%28-9%29*9^k%2Ffactorial%28k%29%2C+k+%3D+0+..+6%29

Answer 4

what does it mean "with continuity correction" I read my text book and I could not find anything mentioning it
Ive already check three times

Answer 5

since they say "approximate the probability" they probably want you to use a normal approximation to the poisson