c) If the initial-state distribution is given by State 1 5 State 2 find TXg, the probability distribution of the system after one observation. 3/4 1/4
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- 1.) The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours which is found to be uniformly distributed. Let x be the time needed to fix an A/C unit. b.) Find the probability that a randomly selected A/C unit repair requires less than 3.5 hours?Question 4 a) A bowl contains six white chips, three red chips and one blue chip. A chip is taken at random from the bowl. Let the random variable X = 1 if a white chip is chosen, let X = 5 if a red chip is chosen and let X = 10 if a blue chip is chosen. Find: i) The probability function f (x) of X. ii) The distribution function F(x) of X. iii) E(X). iv) E(3X² + 5). v) Var(X) b) A discrete random variable X has probability function f (x) = k(x + 1)²,x = 0,1,2. i) Find the value of k. ii) Find E (5X + 3), E (X²) and Var(3X – 2). c) The discrete random variable X represents the number of days spent by a certain 5-х patient in a hospital. The probability function of X is f(x) : -,x = 1,2,3,4. The 10 patient receives $200 from an insurance company for each of the first two days in hospital, and $100 for each day after the first two days. What is the expected amount received?17. Conditional Distributions Consider two random variables X and Y for which we know Pr(X = x) = Pr(X = x|Y = y)for all possible values of x and y. In this case we would say that X and Y are.... Pick ONE option Independent Perfectly correlated Equal to each other More than one of these choices None of these choices
- 10. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period.e. Calculate the probability that there will be a failing student within the first semester.f. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?If A, u are the rates of arrival and departure in an M/M/1 queue respectively, give the formula for the probability that there are n customers in the queue at any time in the steady-state.6. For an insurance coverage, claim counts follow a binomial distribution with m = 4. q varies by insured with the following probabilities: 0.1 0.2 0.3 Probability 0.5 0.25 0.25 An insured submits 0 claims in the first year and 3 claims in the second year. Calculate the predictive probability of the same insured submitting 0 claims in the third year.
- Companies A and B are specialized in installing air conditioners. The number X of service requests that company A receives in a week follows a Poisson distribution with parameter A = 4.5. the Y number of service requests that company B receives in a week obey the following probabilities profile: 2 5 6 3. P(Y=y) 0,05 0,15 0,22 0,22 0,17 0,1 0,05 0,02 a) Which of the two companies receives, on average, the highest volume of orders in a week? Why? b) In which of the two is the variability of the weekly volume of assistance greater? Why? c) Considering the variable Y with a Poisson distribution, calculate the probability that Y is between 1 and 5, and compare with the value obtained by the probability density function of Y. What was observed?3. 4-5 Please solve the following with the provided informationA Florida coastal community experiences a population increase during thewinter months with seasonal residents arriving from northern states and Canada.The postoffice counter has three work stations. The service rate of each postal clerk is 0.75 customerper minute. The anticipated arrival rate is 1.2 customers per minute.Assume that customerarrivals follow a Poisson probability distribution, with an arrival and that service times followan exponential probability distribution. Determine the following operating characteristicsfor the system: d. The average time a customer spends waiting e. The average time a customer spends in the system f. The probability that arriving customers will have to wait for service g. The probability of 5 customers in the system !!!!! 3 WORK STATIONS !!!!
- Part 1 of 6 Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The number of light bulbs that burn out in the next year in a room with 13 bulbs b. The hair color of adults in the United States c. The number of pigeons in a country d. The time it takes for a light bulb to burn out e. The number of free-throw attempts before the first shot is missed f. The number of people in a restaurant that has a capacity of 150 ..... a. Is the number of light bulbs that burn out in the next year in a room with 13 bulbs a discrete random variable, continuous random variable, or not a O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable.1. The following table shows the probabilities associated with the discrete random variable, which counts the number of sales performed at a peak hour in a store in a downtown commercial. It is known that the probability that at most three sales is 40%, that at least five sales are made is 55%, but having less than 6 sales is 63%. one). Find the values of a, b, and c. two). Calculate the cumulative distribution function 3). Find the expectation and variance5. Based on recent records, the manager of a car painting centre has determined the following probability distribution for the number of customers per day: 1 3 4 P(X = x) 0.05 0.2 0.3 0.25 0.15 0.05 А. f the centre has the capacity to serve three customers per day, what is the probability that one or more customers will be turned away on a given day? В. What is the probability that the centre's capacity will not be fully utilized on a day? С. away is no more than 0.1? By how much the capacity must be increased so the probability of turning customer 2. il