Stat 245 Recitation 13 11/1/2007 EA :30am TA: Dongmei Li

Announcement Homework 7 is due on Friday (Nov.2) in lecture. It include following questions from chapter 7: 7.74, 7.76, 7.80, 7.102, 7.104, 7.112, and Homework 6 grades and solutions have been posted on Carmen website. Recitation 12 slides can be found at

Properties of discrete probability distributions For every possible x value, 0  p(X)  1  p(x) =1

Homework problem review 7.18 A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) in applying for a building permit. Let y be number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y; that is, p(y)=ky for y = 1, …, 5. a. What is the value of k? (Hint: Σ p(y) = 1.) b. What is the probability that at most three forms are required? c. What is the probability that between two and four forms (inclusive) are required? d. Could for y=1, 2, 3, 4, 5 be the probability distribution of y? Explain.

Summary Measures of Discrete Random Variable Expected Value Mean of Probability Distribution Weighted Average of All Possible Values May not equal any of the possible values Variance Weighted Average Squared Deviation about Mean Standard deviation

Properties of Mean and Variance

Homework Problem Review 7.40 An appliance dealer sells three different models of upright freezers having 13.5, 15.9 and 19.1 cubic feet of storage space. Let x=the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution: X P(x) a. Calculate the mean and standard deviation of X. b. If the price of the freezer depends on the size of the storage space, X, such that Price = 25X – 8.5, what is the mean value of the variable Price paid by the next customer? c. What is the standard deviation of the price paid?

Quiz about discrete probability distribution atistics_1/0,7233, ,00.utf8.html atistics_1/0,7233, ,00.utf8.html You can only do questions 1 to 9.

Binomial Distribution Number of ‘Successes’ in a Sample of n Observations (Trials) # Reds in 15 Spins of Roulette Wheel # Defective Items in a Batch of 5 Items # Correct on a 33 Question Exam # Customers Who Purchase Out of 100 Customers Who Enter Store # of Bush-Cheney supporters in survey of 100 people

Binomial Distribution Properties 1. Sequence of n Identical Trials 2.Each Trial Has 2 Outcomes ‘Success’ (Desired/specified Outcome) or ‘Failure’ 3.Constant Trial Probability 4. Trials are Independent 5. # of successes in n trials is a binomial random variable

Binomial Distribution? Pick 6 students from this class Each flips a coin Count # of heads Pick 6 students from this class X= # of 1st year students selected Random digit dialing of 100 numbers # of Bush-Cheney supporters Random digit dialing of 100 numbers Sum of ages of respondents

Binomial Probability Distribution Function p(x) = Probability of x ‘Successes’ n=Sample Size p=Probability of ‘Success’ x=Number of ‘Successes’ in Sample (x = 0, 1, 2,..., n)

Binomial Distribution Characteristics n = 5 p = 0.5 n = 5 p = 0.1 Mean Standard Deviation