Exercise

# Exercise 3. Polling - expected value of X-bar

Consider the random variable \(S/N\), which is equivalent to the sample average that we have been denoting as \(\bar{X}\). The variable \(N\) represents the sample size and \(p\) is the proportion of Democrats in the population.

What is the expected value of \(\bar{X}\)?

Instructions

### Possible answers

$$ \mbox{E}(\bar{X}) = p $$

$$ \mbox{E}(\bar{X}) = Np $$

$$ \mbox{E}(\bar{X}) = N(1-p)$$

$$ \mbox{E}(\bar{X}) = 1-p $$