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Q: calculate SN given by Simpson’s Rule for the value of N indicated.
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Q: calculate SN given by Simpson’s Rule for the value of N indicated.
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- 38. Prove or disprove that .Show that A × B ≠ B × A, when A and B are nonempty,unless A = BSuppose in a small town there are three places to eat, a Chineserestaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinnerin one of these places or has dinner at home. Assume that 20% of those who eat inthe Chinese restaurant go to Mexican next time, 20% eat home and 30% go to thepizza place. From those who eat in the Mexican restaurant, 10% go to the pizzaplace, 25% go to the Chinese restaurant, and 25% eats at home next time. Fromthose who eat at the pizza place, 30% eat at home, 30% eat at the Chineserestaurant, and 10% eat at the Mexican restaurant next time. Those who eat athome, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% tothe pizza place. a. Set us the matrix of transition probabilities and show the transition b. Find the steady state probabilities c. In the long run, which restaurant will have the most customer
- Suppose in a small town there are three places to eat, a Chineserestaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinnerin one of these places or has dinner at home. Assume that 20% of those who eat inthe Chinese restaurant go to Mexican next time, 20% eat home and 30% go to thepizza place. From those who eat in the Mexican restaurant, 10% go to the pizzaplace, 25% go to the Chinese restaurant, and 25% eats at home next time. Fromthose who eat at the pizza place, 30% eat at home, 30% eat at the Chineserestaurant, and 10% eat at the Mexican restaurant next time. Those who eat athome, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% tothe pizza place. a. Set us the matrix of transition probabilities and show the transition diagram b. Find the steady state probabilities c. In the long run, which restaurant will have the most customerIt was found that 33% of all diners order vegan meals and that 90% of all diners are undergraduate students. Furthermore, 30% of all undergraduate students order vegan meals. Label the event “diner orders a vegetarian meal” as V and call the event “diner is an undergraduate student” as U. 1. Are V and U independent? 2. Are V and U mutually exclusive? 3. Are V and U collectively exhaustive?Suppose that an experimenter tossed three balanced coins. He defined X1, to denote thenumber of heads and X2, is to denote the amount of money won on a daily lotto bet in SouthAfrica in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. Ifthe first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear,the R1 (that is, win −R1) is lost.Findi) the joint probability function of X1and X2. ii) the probability that less than 3 heads will occur and the student will win R1 or less
- Draw a Venn diagram so that N(U) = 15, n(S) = 10, n(T)= 4, n(SUT) = 13Suppose that an experimenter tossed three balanced coins. He defined X1, to denote thenumber of heads and X2, is to denote the amount of money won on a daily lotto bet in SouthAfrica in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. Ifthe first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear,1the R1 (that is, win -R1) is lost.Findi) the joint probability function of X,and X2-) the probability that less than 3 heads will occur and the student will win R1 or less.A library subscribes to two different weekly news magazines, each of which is supposed to arrive in "Wednesday's mail. In actuality, each one may arrive on "Wednesday, Thursday. Friday, or Saturday. Suppose the two arrive independently of one another, and for each one P(Wed.) = .3, P(Thurs.) = .4, P(Fri.) = .2, and P(Sat.) = .1. Let Y= the number of days beyond Wednesday that it takes for both magazines to arrive (so possible Y values are 0, 1, 2, or 3). Compute the pmf of Y.[Hint: There are 16 possible outcomes; Y(W,W) = o, Y(F,Th) = 2. and soon.]
- 9. Which is true for a non-empty subset s of r?AT&T was running commercials in 1990 aimed at luring back customers whohad switched to one of the other long-distance phone service providers. One suchcommercial shows a businessman trying to reach Phoenix and mistakenly gettingFiji, where a half-naked native on a beach responds incomprehensibly in Polynesian.When asked about this advertisement, AT&T admitted that the portrayed incidentdid not actually take place but added that this was an enactment of something that“could happen.”12 Suppose that one in 200 long-distance telephone calls is misdirected. What is the probability that at least one in five attempted telephone calls reachesthe wrong number? (Assume independence of attempts.)Refer to the information in the previous problem. Given that your longdistance telephone call is misdirected, there is a 2% chance that you will reach a foreign country (such as Fiji). Suppose that I am now going to dial a single long-distancenumber. What is the probability that I will erroneously…Prove that if a=nm with (n,m)=1, then (a,b)=(b,n)·(b,m).