# Thread: Two balanced fair coins

1. ## Two balanced fair coins

I have been in Miami for 10 days; therefore, I can't think at the moment.

Two balance coins are flipped. What are the expect value and variance of the number of heads observed?

Thanks for the help.

2. Originally Posted by dwsmith
Two balance coins are flipped. What are the expect value and variance of the number of heads observed?
The values of the outcomes are $\{0,1,2\}$.
The probabilities are: $\{P(X=0)=0.25,~P(X=1)=0.5,~\&~P(X=2)=0.25\}$

3. Originally Posted by Plato
The values of the outcomes are $\{0,1,2\}$.
The probabilities are: $\{P(X=0)=0.25,~P(X=1)=0.5,~\&~P(X=2)=0.25\}$
I knew it would be easy.

Thanks.

$\displaystyle\text{E}[X]=\sum_xxp(x)=0\cdot\frac{1}{4}+1\cdot\frac{1}{2}+2 \cdot\frac{1}{4}=1$

$\displaystyle\text{Var}[X]=\text{E}[X^2]-\left(\text{E}[X]\right)^2=\frac{3}{2}-1=\frac{1}{2}$