Question

Poisson Distribution:
A small life insurance company has determined that on the average it receives 3 death claims per day. Find the probability that the company receives at least four death claims on a randomly selected day.

Answer 1

can you change the 3 to 6 and the 4 to 7

Answer 2

you have to compute several numbers

Answer 3

at least 4 means not 0, 1, 2, or 3, so you need to compute
\[1-\left(P(x=0)+P(x=1)+P(x=2)+P(x=3)\right))\]

Answer 4

\(P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}\)

Answer 5

in your case \(\lambda = 3\)

Answer 6

\[P(x=0)=e^{-3}\]
\[P(x=1)=3e^{-3}\]
\[P(x=2)=\frac{9e^{-3}}{2}\]
\[P(x=3)=\frac{3^3e^{-3}}{6}=\frac{9e^{-\lambda}}{2}\]

Answer 7

thanks so much for the explanation Satellite 73

Answer 8

yw