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.
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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 $\displaystyle \{0,1,2\}$. The probabilities are: $\displaystyle \{P(X=0)=0.25,~P(X=1)=0.5,~\&~P(X=2)=0.25\}$
Originally Posted by Plato The values of the outcomes are $\displaystyle \{0,1,2\}$. The probabilities are: $\displaystyle \{P(X=0)=0.25,~P(X=1)=0.5,~\&~P(X=2)=0.25\}$ I knew it would be easy. Thanks. $\displaystyle \displaystyle\text{E}[X]=\sum_xxp(x)=0\cdot\frac{1}{4}+1\cdot\frac{1}{2}+2 \cdot\frac{1}{4}=1$ $\displaystyle \displaystyle\text{Var}[X]=\text{E}[X^2]-\left(\text{E}[X]\right)^2=\frac{3}{2}-1=\frac{1}{2}$