Exercise

Exercise 1. Polling - expected value of S

Suppose you poll a population in which a proportion $p$ of voters are Democrats and $1-p$ are Republicans. Your sample size is $N = 25$. Consider the random variable $S$, which is the total number of Democrats in your sample.

What is the expected value of this random variable $S$?

Instructions

50 XP

Possible Answers

$$\mbox{E}(S) = 25(1-p)$$
$$\mbox{E}(S) = 25p$$
$$\mbox{E}(S) = \sqrt{25 p (1-p)}$$
$$\mbox{E}(S) = p$$