WARM UP: Solve the equation for height for an age of 25. Solve for using:

Understanding Randomness Chapter 11 Understanding Randomness An event is RANDOM if we know what outcomes could happen, but not which particular values will happen. The PROBABILITY of any outcome is the proportion of times the outcome would occur in a very long series of repetitions or trials. An event is truly random if the probability of any one event occurring is the same for every outcome. True random outcomes must be INDEPENDENT. Meaning that the outcome of one trial must not influence the outcome of any other trial.

Ways of Generating Random Numbers / Outcomes - Rolling a Die: {1,2,3,4,5,6} Each outcome has a 1/6 chance of occurring. - Tossing a Coin: {H, T} Each outcome has a 1/2 chance of occurring. - TI Graphing Calculator Random Number Generator: {1,2,3,…n} Each outcome has a 1/n chance of occurring. MATH → PRB #5:randInt( 1, n ) - Table of Random Digits: {0,1,2,…,9} Each outcome has a 1/10 chance of occurring if you select one digit at a time or 1/100 if you select two digits at a time. Appendix G A-77 - Slips of paper drawn from a hat: {1,2,…,n} Each outcome has a 1/n chance of occurring. You must replace the slip each time.

The most basic event is called a Component The most basic event is called a Component. Each component has a set of possible randomly occurring Outcomes. Several components = Trial

Simulation Steps Assign numbers to model the outcome. Explain how you will simulate the trial. State clearly what the response variable is. Run several trials. Determine when you Stop!. State your conclusion (in the context of the problem, as always).

HW: Page 266: 1-9, 11 #11. T.W.=0,1; L.A.=2,3,4; S.W.=5,6,7,8,9 1. Assign: Use single digits 0-9 2. Simulate: Use Table of Random Digits. 3. Response: At least 1 of each person out of set of 5, or NOT. 4. Run Trials: Take 5 Random digits at a time, 20 times. 5. Conclusion: % of success.

HW: Page 266: 1-9, 11 #11.

HW: Page 266: 1-9, 11

Page 267 #10 – Simulation Simulate drawing five cards and calculating the probability of getting two pair or three of a kind. The component is picking ONE single card. An outcome is the suit and denomination of the card. This can be done with the table of random digits: Order the cards in the deck giving every card a number {01-52}. Select two digits at a time from a random row in the random digit table. Ignore 00, and 53-99 and numbers that repeat. OR You could go to the table of random digits and select one digit at a time {1,2,3,4} to simulate a Suit and then select two digits at a time {01-13} to simulate a denomination. Ignoring 0, 5-9 for suits and 00, 14-99 for denomination and repeaters. A trial is a collection of 5 randomly selected cards. (5-card hand) The response variable is recording whether the hand has two-pair, three of a kind, or neither.

WARM UP Perform a Linear Regression on the following points and Identify the Slope and Correlation. Remove the Outlier and Identify the new Slope and Correlation. X Y 1 3 4 5 8 7 10 2 9 X Y 1 3 4 5 8 7 10 2 9 Slope (b) = 0.3183 Correlation (r) = 0.4768 Slope (b) = 0.5677 Correlation (r) = 0.9984