Page 199 Probelm 13

The Poisson distribution with parameter λ = .3 has been assigned for the outcome of an experiment. Let X be the outcome function. Find P (X = 0), P (X = 1), and P (X > 1).

The Posison Distribution is given by: \(P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}\)

So, to find \(P(x=0)\) we need to calculate: \(P(x=0)=\frac{.3^0e^{-.3}}{0!}=e^{-.3}=0.7408182\)

Then, \(P(x=1) = \frac{.3^1e^{-.3}}{1!}=.3e^{-.3}=0.2222455\)

To compute \(P(x>1)\) we can find the complement so \(1-P(x=0)+P(x=1)\)

This is equal to: \(P(x>1) = 1 - e^{-.3} + .3e^{-.3}=0.4814272\)

pXEqual0 <- exp(1)^(-.3)
print(pXEqual0)
## [1] 0.7408182
pXequal1 <- .3*exp(1)^(-.3)
print(pXequal1)
## [1] 0.2222455
pXGreaterThan1 <- 1 - pXEqual0 + pXequal1
print(pXGreaterThan1)
## [1] 0.4814272