Consider the Bayesian Network containing three Boolean random variables shown in Figure4. Compute the following : (a). P(~A|W, H). (b). P(~A, W, H). (c). P( ~A|H). W P(W) = 0.2 P(A|~W) = 0.4| A P(H | W) = 0.3 H P(A|W) = 0.8 P(H|-W) = 0.1
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- Find a Hamiltonian circuit in Cay({(1, 0), (0, 1)}:Z4 ⊕ Z6).Assuming that the climate in the city of Metepec behaves according to a Markov chain, consider the following data. The probability of rain on any following day is 70% if it rained the day before, and 20% if it did not rain the day before; Likewise, the probability that the next day will be dry is 80% if the day before was dry, and 30% if it rained the day before. From this information: C. Find the probability that Friday is a dry day, given that it rained today, Tuesday. D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today?A network provider investigates the load of its network. The number of concurrent users is recorded at fifty locations (thousands of people), 17.2 22.1 18.5 17.2 18.6 14.8 21.7 15.8 16.3 22.8 24.1 13.3 16.2 17.5 19.0 23.9 14.8 22.2 21.7 20.7 13.5 15.8 13.1 16.1 21.9 23.9 19.3 12.0 19.9 19.4 15.4 16.7 19.5 16.2 16.9 17.1 20.2 13.4 19.8 17.7 19.7 18.7 17.6 15.9 15.2 17.1 15.0 18.8 21.6 11.9 (a) Compute the sample mean, variance, and standard deviation of the number of concurrent users. (b) Estimate the standard error of the sample mean. (c) Compute the five-point summary and construct a boxplot. (d) Compute the interquartile range. Are there any outliers? (e) It is reported that the number of concurrent users follows approximately Normal distribution. Does the histogram support this claim
- what is the step by step basis taken to solve the following jump discontinuity?In a previous exercise, you were asked to model the following scenario with a directed network. A car rental company has three locations in Mexico City: the International Airport, Oficina Vallejo, and Downtown. Customers can drop off their vehicles at any of these locations. Based on prior experience, the company expects that, at the end of each day, 40% of the cars that begin the day at the Airport will end up Downtown, 40% will return to the Airport, and 20% will be at Oficina Vallejo. Similarly, 70% of the Oficina Vallejo cars will end up Downtown, with 10% returning to Oficina Vallejo and 20% to the Airport. Finally, 30% of Downtown cars will end up at each of the other locations, with 40% staying at the Downtown location. This scenario can also be investigated using a discrete-time population model.Let An, Vn, and Dn be the number of cars at the Airport, Oficina Vallejo, and Downtown, respectively, on day n. Write a system of three equations (as in Example 6.23) giving An, Vn, and…Fifty-four players (including Gabe Kaplan and JamesGarner) participated in the 1980 World Series of Poker.Each player began with $10,000. Play continued until oneplayer had won everybody else’s money. If the World Seriesof Poker were to be modeled as a Markov chain, how manyabsorbing states would the chain have?
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- Determine the classes of the Markov chain and whether they are recurrent.Here is the Markov Chain (enclosed), then… ▪ Which state are communicating?▪ Which are the transient states?▪ The systems are ergodic or non-ergodic? b. Explain about reneging, balking, dan jockeying in queueing theory!c. Please pay attention to the following statements!▪ Statement 1: In making rational decisions, a player needs anticipation of thecompetitor’s response.▪ Statement 2: Competitor’s behaviour can be expected.Are the two above statements true or false?A network provider investigates the load of its network. The number of concurrent users isrecorded at Seventy -seven locations (thousands of people),55.3 55.3 55.3 55.9 55.9 55.9 55.9 56.1 56.1 56.1 56.156.1 56.1 56.8 56.8 57.0 57.0 57.0 57.8 57.8 57.8 57.957.9 57.9 58.8 58.8 58.8 59.8 59.8 59.8 62.2 62.2 63.863.8 63.8 63.9 63.9 63.9 64.7 64.7 64.7 65.1 65.1 65.165.3 65.3 65.3 65.3 67.4 67.4 67.4 67.4 68.7 68.7 68.768.7 69.0 70.4 70.4 71.2 71.2 71.2 73.0 73.0 73.1 73.174.6 74.6 74.6 74.6 79.3 79.3 79.3 79.3 83.0 83.0 83.0i. Construct a grouped frequency distribution for the data using five classes. ii. Compute the sample mean, variance, and standard deviation of the number ofconcurrent users.iii. Construct a frequency histogram for the datab) It is reported that the number of concurrent users follows a positive skew distribution.Does the histogram support this claim?