Question

In the average there are 2 suicides.if 1 month equal to 30 days find the probability that:at least 5 suicides

Answer 1

Poison distribution

$P(X\ge5)=1-P(4)-P(3)-P(2)-P(1)-P(0)\\P(x)=\frac{e^{-\lambda}\lambda^x}{x!}$

$\lambda=2$

$P(X=4)=\frac{e^{-2}2^4}{4!}=0.09$

$P(X=3)=\frac{e^{-2}2^3}{3!}=0.18$

$P(X=2)=\frac{e^{-2}2^2}{2!}=0.27$

$P(X=1)=\frac{e^{-2}2^1}{1!}=0.27$

$P(X=0)=\frac{e^{-2}2^0}{0!}=0.135$

$P(X\ge5)=1-0.09-0.18-0.27-0.27-0.135=0.055$