Problem 5: 10 points Assume that a mumber N of phone calls handled by a customer...
Problem 6: 10 points John is a customer service representative who responds to the calls. The number of calls during one shift is (N + 1), where is Poisson distributed with the expected value-λ = 24, the duration, U, of a single call (in minutes) is uniformly distributed over the interval (2,8) N+1 Suppose that T- X, represents the actual time spent by John with customers on the phone. 1. Evaluate the average busy time, E T], for John 2....
Problem 5: 10 points Assume that a discrete random variable, N, is Poisson distributed with the rate, λ = 3. Given N = n, the random variable, X, conditionally has the binomial distribution, Bin [N +1, 0.4] 1. Evaluate the marginal expectation of X. 2. Evaluate the marginal variance of X
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the...
1. A salesperson has successes on 2 out of 10 cold calls. What is the probability of getting 3 successes in 9 cold calls? 2. If the probability of success on a cold call is .20, and 500 cold calls are made, what is the probability of less than 84.5 successes? (use normal distribution to approximate the binomial, so need mean = np and st.dev = sqrt(npq) ) 3. In the past, the probability of success of a cold call...
Problem 6: 10 points Assume that observable is a random variable W = min X, <i<5 where {X; : 1<i<5} are independent and uniformly distributed on the unit interval (0 < x < 1). 1. Derive CDF for W, that is F(w) = PW <w]. 2. Evaluate density function, f(w) and identify it. 3. Find expected value of W. 4. Determine variance of W.