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

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