Chapter 2 Section 3 Question 3

Question

Consider flipping two fair coins. Let X = 1 if the first coin is heads, and X = 0 if the first coin is tails. Let Y = 1 if the second coin is heads, and Y = 5 if the second coin is tails. Let $Z = XY$. What is the probability function of Z?

Answer

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

$$p\scriptsize{Z}\normalsize{(0) = \frac{1}{2}}$$ $$p\scriptsize{Z}\normalsize{(1) = \frac{1}{2}*\frac{1}{2}=\frac{1}{4}}$$ $$p\scriptsize{Z}\normalsize{(5) = \frac{1}{2}*\frac{1}{2}=\frac{1}{4}}$$ $p\scriptsize{Z}\normalsize{(z)=0}$ for all $z\notin\{0,1,5\}$

$$p\scriptsize{Z}\normalsize{(0) = \frac{1}{2}}$$ $$p\scriptsize{Z}\normalsize{(1) = \frac{1}{2}*\frac{1}{2}=\frac{1}{4}}$$ $$p\scriptsize{Z}\normalsize{(5) = \frac{1}{2}*\frac{1}{2}=\frac{1}{4}}$$ $p\scriptsize{Z}\normalsize{(z)=0}$ for all $z\notin\{0,1,5\}$