Chapter 12.5, Problem 38E

(a)

To determine

To verify: The function ${\displaystyle \sum _{x=1}^{\infty }f\left(x\right)=1}$ using equation $f\left(x\right)={\left(1-p\right)}^{x-1}p$ where $x=1,2,3,\dots$.

(b)

To determine

The expected value for function ${\displaystyle \sum _{x=1}^{\infty }xf\left(x\right)}$ using equation $f\left(x\right)={\left(1-p\right)}^{x-1}p$ where $x=1,2,3,\dots$.

(c)

To determine

The number of major league baseball players to meet before meeting one who is foreign born.

(d)

To determine

The probability to meet a foreign-born player within the first three major league players.