(a) P= State 0 123 00012 о го о 33 11 0 0 0 20100 3010 3 0 1 0 0 State 0123 0 [1000] 01 0 1 2 2 (b) P = 20 0 1 0 22 3 00
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Given the following (one-step) transition matrices of a Markov chain, determine the classes of the Markov
chain and whether they are recurrent.
![(a) P=
State 0 123
00012
о го о
33
11 0 0 0
20100
3010
3 0 1 0 0
State
0123
0 [1000]
01 0
1
2 2
(b) P =
20
0
1
0
22
3
00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71a93994-cfe8-4bd0-bacf-87e96face337%2F24cd77de-a83b-45ac-a493-073f3e9e153a%2F6qkyhln_processed.png&w=3840&q=75)
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- n alpha=0.05 alpha=0.014 0.950 0.9905 0.878 0.9596 0.811 0.9177 0.754 0.8758 0.707 0.8349 0.666 0.79810 0.632 0.76511 0.602 0.73512 0.576 0.70813 0.553 0.68414 0.532 0.66115 0.514 0.64116 0.497 0.62317 0.482 0.60618 0.468 0.59019 0.456 0.57520 0.444 0.56121 0.433 0.54922 0.423 0.53723 0.413 0.52624 0.404 0.51525 0.396 0.50526 0.388 0.49627 0.381 0.48728 0.374 0.47929 0.367 0.47130 0.361 0.46335 0.334 0.43040 0.312 0.40345 0.294 0.38050 0.279 0.36155 0.266 0.34560 0.254 0.33065 0.244 0.31770 0.235 0.30675 0.227 0.29680 0.220 0.28685 0.213 0.27890 0.207 0.27095 0.202 0.263100 0.197 0.256A random sample of 80 poultry farms of one variety gave an average production of 240 eggs per bird. Another random sample of 50 poultry farms of another variety gave an average production of 195 eggs per bird. At a=0.05 is there sufficient evidence to support that there is a significant difference between the egg production of the two varieties of birds. Assume o1 =18 eggs and o2=15 eggsA certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. x2 0 1 2 3 x1 0 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 2 0.05 0.03 0.10 0.06 3 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.06 (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line?P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical?P(X1 = X2) = (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X1 and X2. A = {X1 ≥ 2…
- An experimenter is studying the effects of temperature,pressure, and type of catalyst on yield from a certainchemical reaction. Three different temperatures, fourdifferent pressures, and five different catalysts are underconsideration.a. If any particular experimental run involves the use ofa single temperature, pressure, and catalyst, howmany experimental runs are possible?b. How many experimental runs are there that involve useof the lowest temperature and two lowest pressures?c. Suppose that five different experimental runs are tobe made on the first day of experimentation. If thefive are randomly selected from among all the possibilities,so that any group of five has the same probabilityof selection, what is the probability that adifferent catalyst is used on each run?In a Wilcoxon Mann Whitney test n1 is 9 and nprime is 7. What are the correct values for K1 and K2 ? K1 = 36 and K2 = 26 K1 = 35 and K2 = 26 K1 = 36 and K2 = 27 K1 = 35 and K2 = 30Question 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…
- What is the coefficient of x^n for the generating function (1)/(1+x)^2?Two groups of students are given a problem-solving test, and the results are compared. Group 1 Group 2 1 = 83.6 = 79.2 s1=4.1 s2=3.9 n1=36 n2=36 At α= 0.01, can it conclude that there is a significan difference in means of two groups? Explain with the 5 steps of hypothesis-testing.14) A) A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 4-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. x 1 2 3 4 p(x) 0.3 0.5 0.1 0.1 Compute V(X). B) Similar to qustion A), a chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 4-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. x 1 2 3 4 p(x) 0.3 0.5 0.1 0.1 Compute the expected number of pounds left after the next customer's order is shipped. [Hint: The number of pounds left is a linear function of X.]
- A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) fY|2 4) E(x)Show all workA manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) E(x)4) E(Y|X=2)5) V(Y|X=2)6) Are X and Y independent? Why?7.) Several years ago, the US began running out of telephone numbers. Telephone companiesintroduced new area codes and numbers were used up, and eventually almost all area codes wereused up. *Please only answer question F. (a) Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0or 1. How many such area codes are possible? (b) The actual number of area codes under this system was 152. What could be the cause of thediscrepancy between this number and your answer to part (a)? (c) A 7-digit telephone number that follows the area code cannot start with a 0 or 1. How manysuch 7-digit telephone numbers are possible in each area code?(d) Under the old area code system in part (a), how many total possibilities are there for areacode with telephone number?(e) The shortage of area codes was resolved by removing the restriction on the second digit of thearea code. (This resulted in problems for some older equipment which used the second digit…
