Chapter 6: Random Variables Section 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 4th edition – For AP* STARNES, YATES, MOORE

Chapter 6 Random Variables 6.1 Discrete and Continuous Random Variables 6.2 Transforming and Combining Random Variables 6.3 Binomial and Geometric Random Variables

Chapter 6 Random Variables Warm-up (3 minutes) Using complete sentences, answer these 2 questions and turn your answers in on the cart.

Remember the difference between DISCRETE and CONTINUOUS variables. It makes a BIG difference when you type it into your calculator.

15 Minutes: Page 409-410 #1-10 Enter your answers in the Socrative App. Keep track of which ones you miss. Late flash cards, reading guides & Class Dojo papers go on the table at the back of the room Get ready for homework questions.

Chapter 6 Random Variables AP Exam Tip If the mean of a random variable has a non-integer value, but you report it as an integer, your answer will be marked as incorrect. AP Exam Tip To get full credit for the “Expected Value”, you need to show the first few terms of the formula. For example: E(X)= 0(.2) + 1(.6) + … + 8(.01) AP Exam Tip Why do we always ADD variances and never subtract? Because MORE variables means MORE variability. And so we ADD the variances.

Chapter 6 Random Variables AP Exam Tip If you are unsure of how to start a free response question on the AP exam, check to see if it has a Binomial setting. AP Exam Tip You will not be expected to calculate a binomial coefficient by hand on the AP Exam. But you will probably have to understand how to substitute values into the formula.

Chapter 6 Random Variables AP Exam Tip The formula for geometric probability is NOT on the formula sheet. However, geometric probabilities can be found using the calculator. AP Exam Tip On many questions involving Binomial settings, students do not recognize that using the binomial distribution is appropriate. In fact, free response questions about the binomial distribution are often among the lowest scoring questions on the exam. Make sure you can identify a binomial distribution. And if you are stumped as to how to start a FRQ, check to see if it is binomial.

Chapter 6 Random Variables AP Exam Tip When students are asked about the effect of a linear transformation on summary statistics, some students forget that adding (subtracting) a constant to (from) every value in the distribution has NO effect on measures of SPREAD, including the standard deviation, variance, range and IQR. AP Exam Tip On the AP exam, many students lose credit when combining two or more random variables because they add the standard deviations instead of adding the variances.

Chapter 6 Random Variables AP Exam Tip When you solve problems involving random variables, start by defining the random variable of interest. For example, Let X = the Apgar score of a randomly selected baby or let Y = the height of a randomly selected young woman. Then state the probability you are trying to find in term of the random variable P(X>7) or P(68<Y<70)

Chapter 6 Random Variables AP Exam Tip Don’t rely on “calculator speak” when showing your work on FRQ. Writing binompdf(5, .25, 3) = .08789 will NOT earn you full credit. At the very least, you must indicate what each of those calculator inputs represents. For example, “I used binompdf on my calculator with n=5, p=.25 and k=3” Better yet, show the binomial probability formula with these numbers plugged in. Or Best of ALL, write it EXACTLY how I showed you in class :)

Chapter 5 Probability: What Are the Chances? “Strive For a 5”: Orange Book top shelf on the case at the back of the room (get the number that matches the number of your text book) Read/do pages 105-125 (DO NOT WRITE IN THIS BOOK) You will take this book home to study in tonight and you will return it tomorrow before the test. We will go over our chapter 5 tests. We will collect data with our pennies (you will need that ½ sheet of paper for the pennies).

Looking Ahead… In the next Chapter… We’ll learn how to describe sampling distributions that result when data are produced by random sampling. We’ll learn about Sampling Distributions Sample Proportions Sample Means In the next Chapter…