Chapter 72 Means and Variances of Random TeacherWeb72章均值與方差的隨機teacherweb

1、chapter 7.2chapter 7.2 warm up do #s 36,39,42 homework due 12/16th and 12/19th # 37,38, 44, 45, 46, 55, 56, 57, 61, 68 pop mini quiz fri/mon review worksheet over break chapter 7 quiz on jan 4th and jan 5thchapter 7.2 means chapter 7.2 means and variances of and variances of random variablesrandom v

2、ariablesnotations notations the mean, finding the mean of a finding the mean of a discrete random variable.discrete random variable. write the distribution like this: to find 1122xiikkx px px px pvalue of x: x1x2. xkprobability: p1p2. pkfinding the variance of a finding the variance of a discrete ra

3、ndom variable.discrete random variable. write the distribution like this: variance is found by:value of x: x1x2. xkprobability: p1p2. pklaw of large numbers:law of large numbers: draw independent observations at random from any population with finite mean rules for means:rules for means: rule 1. if

4、x is a random variable and a and b are fixed numbers, then:rules for variances:rules for variances: rule 1. if x is a random variable and a and b are fixed numbers, then:rules for variancerules for variance if x and y have a correlation chapter 7.2chapter 7.2 warm up do #s 36,39,42 homework due 12/1

5、6th and 12/17th # 37,38, 44, 45, 46, 55, 56, 57, 61, 68 pop mini quiz fri/mon review worksheet over break chapter 7 quiz on jan 4th and jan 5thwarm up 12/16 and 12/17warm up 12/16 and 12/17 at a large university students have either a final exam or a final paper at the end of a course. the table bel

6、ow lists the distribution of the number of final exams that students at the university will take, and their associated probabilities. what are the mean and standard deviation of this distribution (remember to show all work)?x0123p(x)0.050.250.400.30extra examples: #1extra examples: #1 suppose you bu

7、y a raffle ticket at the fair. the ticket costs $1 and the prize is a new truck. the new truck is valued at approximately $22,000. second prize is a $100 gift certificate to southpoint mall. the fair sells 50,000 raffle tickets. what are your average winnings per ticket? make a probability distribut

8、ion table to represent, x, the payoff. the probability the probability distribution of x is :distribution of x is : payoffx:$0$100$22,000 probability: 49998/500001/50000 1/50000 (.99996)(.00002)(.00002) so, the average long-run payoff is ($0*.99996)+($100*.00002)+($22,000*.00002) = $0.442does this m

9、ake sense? does this make sense? it does if you consider the long run. also you could think about it from the fairs point of view. from their side you can see that they pay out an average of 44 cents per raffle ticket sold. further, you could figure their cost to be .442 * $1(50000 tickets sold) = $

10、22,100 further, you could figure their profit to be (1-.442) * $1(50000 tickets sold) = $27,900another example #2 another example #2 finding an expected value.finding an expected value. in 1993, there were 121,100,000 cars in use in the united states. that year, there were 14,100,000 automobile acci

11、dents. the average premium paid in 1993 for automobile collision insurance was $638, and the average automobile collision claim paid by insurance companies was $1796. what was the expected value of the insurance coverage for a person who paid $638 for collision insurance in 1993? solution: let event

12、 a represent having an automobile accident. then event a represents not having an automobile accident. in 1993, the probability of having an automobile accident was: p(a) = which means p(a) 0.884. you can calculate the payoffs for a and a as follows. if the person had an accident, he or she paid $638 and received $1796, so the person received $1796 - $638 = $1158. 14,100,0000.116121,100,000 if the person didnt have an accident, he or she paid $638. thus the expected value was the $429.66