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- 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)A random number generator selects two integers from 1 to 30. What is the probability that both numbers are less than 12?Suppose that the number of accidents occurring on a highway each week is a Poisson random variable with parameter lambda(λ) = 7. a) What is the probability that there there are at least 4 accidents in a week? b) Given that at least one accident occurs in a week, what is the conditional probability that the accident occurs 5 times or less in a week?
- Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 38.~if calls to your cell phone are a Poisson process with a constant rate lambda=2 calls per hour, what's the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? ~How many phone calls do you expect to get during the movie?Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 26.
- Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with parameter λ=3.a) Find the probability that 3 or more accidents occur today.b) Repeat part (a) under the assumption that at least 1 accident occurs today.A bank branch receives an average of 7 complaints per hour from its customers. Using the Poisson formula, find the probability that on a certain day this bank will receive exactly 8 complaints per hour: Will receive at least 3 complaints in three hours: Will receive at most 3 complains in three hours3 - It is stated that 1% of electronic parts produced in a factory are defective. Using the Binoma Poisson approach, calculate the probability that exactly two of the 230 pieces randomly selected from the production line of this factory will be defective.A) 0.2022B) 0.2033C) 0.2652D) 0.2044E) 0.2663
- A traffic enforcer counts the nunber of vehicles at a specific locationin the highway. In his counting, there are 420 vehicles arriving in a span of 1 hour. Assuming that the arrival of vehicles is poisson distributed, estimate the probabilities of having 7 vehicles arriving over a 30-second time interval, over the next 1 minute.Suppose that only 0.1% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 4,000 computers.a. Can you use Poisson distribution as approximation for binomial? Why? b. Compute P(4<=X<=6) (Use the formula of the pmf).Find the moment-generating function of the negativebinomial distribution by making use of the fact that if k independent random variables have geometric distribu-tions with the same parameter θ, their sum is a random variable having the negative binomial distribution withthe parameters θ and k.