The mean of a Poisson random variable X is μ = 9. Compute
P(μ-2σ < X < μ + 2σ).
My reasoning is as follows:
P(9-2(9) < X < 9 + 2(9)) = P(-9 < X <27) . This is all I can think about doing at the moment. Feedback would be appreciated.
The mean of a Poisson random variable X is μ = 9. Compute
P(μ-2σ < X < μ + 2σ).
My reasoning is as follows:
P(9-2(9) < X < 9 + 2(9)) = P(-9 < X <27) . This is all I can think about doing at the moment. Feedback would be appreciated.
$\displaystyle \sigma^2 = 9 \Rightarrow \sigma = \sqrt{9} = 3$.
Calculate $\displaystyle \Pr(3 < X < 15) = \Pr(4 \leq X \leq 14)$. There's no easy way of doing this by hand - you just have to calculate each probability and then add them all up.
You might be able to use the rule of thumb .... It will depend on what accuracy is required.
That's correct to 4 places. F(14)=.9585 and F(3)=.0212.
The difference is .9373. Note that
$\displaystyle F(14)=P(X=0)+P(X=1)+\cdots +P(X=14)$
and
$\displaystyle F(3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)$.
If you want to sum these 11 probabilities, one thing you should do is factor out the common term $\displaystyle e^{-\lambda}$