Chapter 12.5, Problem 37E

(a)

To determine

To verify: The function ${\displaystyle \sum _{x=0}^{\infty }f\left(x\right)=1}$ using equation $f\left(x\right)=\frac{{\lambda }^x{e}^{-\lambda }}{x!}$ where $x=0,1,2,\dots$.

(b)

To determine

The expected value for function ${\displaystyle \sum _{x=0}^{\infty }xf\left(x\right)}$ using equation $f\left(x\right)=\frac{{\lambda }^x{e}^{-\lambda }}{x!}$ where $x=0,1,2,\dots$.

(c)

To determine

The probability in a random sample of 1000 births if there were fewer than 4 cases of infant mortality.