2 Example Population Mean

Suppose that a coin is flipped and \(X\) is declared between 0 or 1 corresponding to a head or a tail, .

What is the expected value of \(X\)?

\[E[X] = .5(0) + .5(1) = 0.5\]

Here, the expected value is one that the coin cannot even take.

What about a biased coin?

2.1 Example

Suppose that a random variable \(X\) is so that \(P(X=1)=p\) and \(P(X=0)=(1-p)\)

\[E[X]=0(1-p)+1(p) = p\]

Suppose that a die is rolled and \(X\) is the number face up. What is the expected value of \(X\)?

\[E[X] = \frac{1}{6}(1)+\frac{1}{6}(2)+\frac{1}{6}(3)+\frac{1}{6}(4)+\frac{1}{6}(5)+\frac{1}{6}(6) = 3.5\]