The process C is defined by C= A | B, where A and B are defined by A = a.0 B =ā.0 a. What are the three ways in which C can evolve? b. Draw the transition graph (and carefully label which one is which) of the process P= A|A|B|B.
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- Use the attached transition diagram to answer the following questions: a. State the transition matrix T and calculate T2 b. i) What percentage of this week's fully fit hockey team players are expected to be fully fit next week? ii) What percentage of the hockey team players that are getting treatment this week are expected to fully fit in two weeks' time?The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) What is ?? b) Write out the formula for the probability distribution of the random variable r. P(r) = _________ c) Find the probability that one otter will initiate social grooming four or more times during the 30-minute observation period. (Round your answer to four decimal places.)In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) Find the probabilities that in your 30 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.) P(4) = P(5) = P(6) = b) Find the probability that one otter will initiate social grooming less than four times during the 30-minute observation period. (Round your answer…
- In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 40 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 40-minute interval) one otter initiates social grooming of another. Lambda = 6.8 (b) Find the probabilities that in your 40 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.) P(4) = P(5) = P(6) =A certain reaction was run several times using each of the two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product.Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows:Catalyst A Catalyst B4.4 3.4 2.6 3.8 3.4 1.1 2.9 5.54.9 4.6 5.2 4.7 6.4 5.0 5.8 2.54.1 2.6 6.7 4.1 3.7 3.8 3.1 1.63.6 2.9 2.6 4.0 3.5 5.9 6.7 5.24.3 3.9 4.8 4.5 6.3 2.6 4.3 3.84.4 3.1 5.7 4.5a. Construct comparative boxplots for the yields of the two catalysts and explain the role the whisker plays in data analysis. b. Interpret what the box plot for catalyst B, communicate in real life? marc. In your own words, give a simple explanation on why statisticians think the sample variance is biased estimator of the population variance and how it could be corrected.Consider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.
- Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 55 clam shells in February and 55 clam shells in March. 14 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months; specifically, if the population proportion in February is higher than March. Let ? = 0.1.Note: Do all calculations as February - MarchA) The point estimate for the true difference in proportion of dark growth bands between February and March is: Note: answer using 4 decimal precisionB) The test statistic, ztest, is: Note: answer using 2 decimal…Let {N_1(t)} and {N_2(t)} be two independent Poisson processes with rates λ1=1 and λ2=2, respectively. Find the probability that the second arrival in N_1(t) occurs before the third arrival in N_2(t). Round answer to 4 decimals.
