Chapter 2 Section 2 Question 1
Question
Consider flipping two independent fair coins. Let X be the number of heads that appear. Compute $P(X=x)$ for all real numbers x.
Answer
Author: Mohammad-Ali Bandzar| Date:Oct 14 2020
The possible outcomes from flipping two coins are as follows:
Heads,Heads
Heads,Tails
Tails,Heads
Tails,Tails
The probability of no heads is $\frac{1}{4}$ therefore $P(X=0)=\frac{1}{4}$
The probability of one head is $\frac{1}{2}$ therefore $P(X=1)=\frac{1}{2}$
The probability of two heads is $\frac{1}{4}$ therefore $P(X=2)=\frac{1}{4}$
the probability of any other number of heads is zero $P(X=x)=0$ for $x\notin \{0,1,2\}$