AP Statistics CH 6 Review Discrete Random Variables: Section 6.1 Page 342 has properties of discrete random variables. Discrete random variables take on isolated values on the number line. The mean of a discrete random variable is x xi p( xi ) (see pp. 345-46 example) The standard deviation of a discrete random variable is (x i x ) 2 p( xi ) (See p. 347 with example) See p. 348 for calculator commands to help calculate the mean and standard deviation, but remember you must show the calculations. It is satisfactory to write down the first two values, then … + the last value as shown in class. Continuous Random Variables: Section 6.1 Read pp. 349-353 Transforming and Combining Random Variables: Section 6.2 Understand the properties in this section. See summary on page 377. Read the examples in this section as needed. AP Problems: 2002B#2 (Airline Problem), 2008#3 (Arcade Problem), 2005#2 (Telephone Problem), 2002B#2 (Concert Problem), 1999#5 (see attached problem), 2007B#2 (Pet Problem), 2001#2 (Copier Problem) 2008#3 Binomial Distributions: Section 6.3 The Binomial Setting o Each observation falls into one of 2 categories (success or failure) o The n observations are all independent. o The probability of success (called ) is the same for each observation o There is a fixed number n of observations. n Binomial formula P( X k ) p k (1 p) n k , where k arrange k successes among n observations. n n! is k k!(n k )! the number of ways to x np and np(1 p) if the distribution is binomial. See p. 389 for more detailed calculator commands and examples. Binompdf(n, p, k) gives the probability of getting exactly x successes in k trials, if the probability of success on each trial is p. Binomcdf(n, p, k) gives the probability of getting at least x successes in k trials, if the probability of success on each trial is p. AP Problems: 2003#3, 2004#3, 2009#2, 2007B#2, 1999#4, 2006B#6 Geometric Distributions: Section 6.3 The Geometric Setting o Each observation falls into one of 2 categories (success or failure) o The observations are all independent. o The probability of success (called p) is the same for each observation o The variable we’re interested in is the number of trials until the 1st success is obtained Geometric formula P( X k ) (1 p)n 1 p and x 1 p See p. 400 for more detailed calculator commands and examples. Geometricpdf(p, k) – this is used to find the probability that you’re 1st success will be on the kth trial. Geometriccdf(p, k) – to find the prob. That you get your 1st success by at least the kth trial. Normal Distributions are a type of continuous random variable and are covered in both Chapter Two Section Two and Chapter Six You should be able to calculate z-scores and the associated probability. You should be comfortable with the calculator commands or using the chart. You should be able to find a zscore and value of x if you know a given probability. See Section 2.2 for examples. z x See p. 123 & 124 for more detailed calculator commands and examples. Normalpdf is used when you want to graph a normal curve. Normalcdf (lower bound, upperbound) is used when you want to find the probability when you now the z-score. Normalcdf (lower bound, upperbound, , ) is also an option if you have the original values. Invnorm(area to left) calculates the associated z-score. Invnorm(area to left, , ) calculates the associated data value if you enter the mean and standard deviation. AP Problems: 2002#3, 2007#3, 2009#2, 2004B#3, 2005B#6, 2008B#5, 2008B#5, 2000#6, 2006B#3 Checking for Normality: Section 2.2 See pages 124-128 To determine if data is approximately normal, use the normal probability plot. If the normal probability plot is approximately linear, then the data is approximately normal. You must sketch the normal probability plot on the AP test and write the sentence above.