1. 7.4 The Mean The means were 2.62 and 2.56. – What does this say in relation to the problem? What was the theoretical expectation? – This is also call the EXPECTED VALUE The expected value is what should happen over the long run. – Law of Large Numbers!! Number of Heads in 5 tosses of a Coin Frequency 03 119 226 329 417 56 Number of Heads in 5 tosses of a Coin Frequency 01 19 212 318 46 54

2. 7.4 The Mean Find the Expected Value ValueProbability -20.2 0.35 00.05 10.15 20.25 Word Problem! You receive all your test grades back for the first semester in a certain class: 90, 85, 90, 75, 85, 90, 85, 75, 90, 85 – Find your average score by adding them all up and dividing by 10. – Create a frequency table from the information. – Find the mean using the frequency table. Is this theoretical or experimental? Why is this theoretical?

3. 7.4 The Mean Mean vs. Expected Value Both Mean and the Expected Value are calculated the same. The difference is from the information you are given – Is this actual data? MEAN – Is this what should happen? EXPECTED VALUE The following table give the possible returns of two different investments. Calculate the expected value of each. Which investment has the greater expected return? Investment A ReturnProbability $10000.2 $20000.5 $30000.3 Investment B ReturnProbability -$30000.1 00.3 $40000.6

4. 7.4 The Mean Let’s make some money… Don Dollars that is! There’s a new game out at the local casino. The game is one-on- one with another person. You (person 1) roll a dice. If it lands on an odd number, person 1 pays person 2 $1 for each dot on the upper most side. If it lands on an even number, person 2 pays person 1 $1 for each dot on the upper most side. Now, the repeat the steps swapping rolls. – Person 1 becomes person 2 and vice versa. Calculate the expected value of this game. Now, play the game. How do you do?

5. 7.4 The Mean Problems to complete for homework from section 7.4 Pg. 364#1 – 5