In the event that Xi, I = 1, 2, 3 are autonomous remarkable arbitrary factors with rates Ai = 1, 2, 3, find (a) P{Xi

(b) P{X1

(C) EIMaXXilKi

(d) ElmaxXil

Q14

A bunch of n urban areas is to be associated through correspondence joins. The expense to build a connection between urban communities I and j is Cap I r j. Enough connections ought to be built so that for each pair of urban areas there is a way of connections that interfaces them. Therefore, just n ? 1 connections need be developed. An insignificant expense calculation for tackling this issue (known as the negligible crossing tree issue) first develops the least expensive of all the (1 ) joins. At that point, at each extra stage it picks the least expensive connection that associates a city with no connections 3, , n to one with joins. That is, assuming the principal connect is between urban areas 1 and 2, the subsequent connection will either be somewhere in the range of 1 and one of the connections or somewhere in the range of 2 and one of the connections 3, .. , n. Assume that the entirety of the (11) costs are free remarkable irregular factors with mean 1. Track down the normal expense Cu of the former calculation

in the event that

(a) n = 3,

(b) n = 4

Q15

Leave X1 and X2 alone free outstanding irregular factors, each having rate p. Let X(i) = minimum(Xi, X1) and X(2) = IMU M( X , X>) Find

(a) EIX(1)1. (b) Var[Xi), (c) EIX1)], (d) Var[Xz],

Q16

Consider a two-worker framework where a client is served first by worker 1, at that point by worker 2,

and afterward withdraws. The assistance times at worker j are outstanding arbitrary factors vvith rates I =

1, 2. At the point when you show up, you discover worker 1 free and two clients at worker 2?customerA in

administration and client a holding up in line.

(a) Find PA, the likelihood that An is as yet in setuice vvhen you move over to worker 2.

(b) Find PS, the likelihood that B is as yet in the framework when you move over to worker 2.

(c) Find EITI, where Tis the time that you spend in the framework.

Clue: Write

where is your setuice time at worker I, WA is the measure of time you stand by in line while An is

being sawed, and WE is the measure of time you stand by in line vvhile B is being served.

During 2010, the United States performed its every-ten-year census. Suppose that the Census Bureau sampled (names generated by the computer, with replacement) 1000 residents of Massachusetts (population: 6,000,000) and asked them to fill out a more detailed census form. Let X = the number of people in this sample who live in the greater Boston (Massachusetts) area (population: 2,000,000). Then (circle your answer and explain your choice); (a) X is a binomial random variable with n = 6, 000, 000 and 0 = =. (b ) X is not a binomial random variable since the events "Massachusetts resident" and "greater Boston resident" are not independent. (c) X is a binomial random variable with n = 1000 and 8 = 2. (d) X is not a binomial random variable because there are more than two outcomes with respect to where a person might live. (e) X is a binomial random variable with n = 1000 and d = 60008. Gro-More Pet Food has a 16% market share. Assume the probability a customer will buy Gro- More is 16%. A sample of 24 customers is selected. a) Consider a binomial random variable X indicating the number of customers in a sample of 24 who will buy Gro-More. What values can the random variable assume? b) Find the probability that exactly eight customers in the sample of 24 will buy Gro-More. Express your answer to four places after the decimal point. c) Find the probability that at least three customers out of the sample of 24 will buy Gro-More. Express your answer to four places after the decimal point. d) Find the expected value of the random variable X. e) Find the standard deviation of the random variable X.Fifteen percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent? (Use normal approximation to the binomial distribution to answer this question) 5a) A University found that 20% of the students withdraw without completing the introductory statistics course. Assume that 20 students registered for the statistics course. . has un a) Compute the probability that two or fewer students will withdraw. b) Compute the expected number of withdrawals. 5b). In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. What is the probability that the sample contains between 12 and 14 business majors?Bart and Lisa Simpsons take a Statistics class. The chance that Bart passes Statistics is 30%. The chance that Lisa passes Statistics is 80%. Let X be the number of Simpsons that pass Statistics. 1. Set up the table of distribution and cumulative distribution of X. (A probability tree may be helpful.) 2. Calculate the expected value and standard deviation of X. 3. How likely is it that exactly one of the two passes