Two balanced fair coins

**dwsmith** · March 15th 2011, 08:28 AM

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.

**Plato** · March 15th 2011, 08:38 AM

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: $\{P(X=0)=0.25,~P(X=1)=0.5,~\&~P(X=2)=0.25\}$

**dwsmith** · March 15th 2011, 08:40 AM

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.

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

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

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