Chapter 2 Section 3 Question 2

Question

Consider flipping a fair coin. Let Z = 1 if the coin is heads, and Z = 3 if the coin is tails. Let $W = Z^2 + Z$.

- What is the probability function of Z?
- What is the probability function of W?

Answer

Author: Mohammad-Ali Bandzar| Date:Oct 15 2020

- (a) What is the probability function of Z?
- $$p\small{Z}(1) = \frac{1}{2}$$ $$p\small{Z}(2) = \frac{1}{2}$$ $p\small{Z}(z)=0$ for all $z\notin\{1,2\}$

- (b) What is the probability function of W?
- $$p\small{W}(2) = p\small{Z}(1)=\frac{1}{2}$$ $$p\small{W}(12) = p\small{Z}(3)=\frac{1}{2}$$