# Practice Problems - Random Variables, Averages, and Statistics

## Expected Value - Jewelry - from 4.2

Erin has 5 chains in a jewelry box: 4 silver chains worth \$40 each, and 1 gold chain worth \$2500. She selected a chain at random to wear for her midterm exam. What is the expected dollar value of the chain selected?

## Expected Value - Committee - from 4.2

A class consist of 8 sophomores and 4 juniors. Two students are selected at random to form a committee. Find the expected number of juniors on this committee.

## Expected Value with Bernoulli - What's your number? - from 4.2

When Dan asks a girl for her phone number, he has a 30% chance of getting it (what a pimp!). He asks 100 girls for their number Friday night. Considering that each girl does not base her decisions on any other girl’s decisions, what is the expected number times he get rejected on Friday night?

## Expected Value - Selecting Coins - from 4.2

I have 2 nickels and 3 quarters in my pocket. I pick two out simultaneously at random, and a random variable X is defined to be the total value of the two coins selected. Find the expected value of X.

## Expected Value - Fill in the Blanks - from 4.2

A random variable X has the following probability density function:

The expected value of X is 0.7. Find a and b

## Expected Value - Lottery Tickets - from 4.2

A lottery ticket cost \$1. One in one hundred tickets is a \$40 prize, and one in one thousand tickets is a \$400 prize. What is the expected payoff of purchasing one ticket? (payoff is the winnings of the ticket minus the cost)

## Expected Value with Bernoulli - Unfair Coin - from 4.2

An unfair coin is flipped 10 times. On each toss, the probability of getting a head is 0.7. Let a random variable X equal to the number of heads minus the number of tails. Find E(X).