Hospital Emergency room accepts an average of about 28 bone fracture patients a week that requiredajesources available with this demand accordingly. What is the probability that on any given day no more than one fracture patients arrive at the emergency room?
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- Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hoursQuestion 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will be y − L. The chance of a safe return is 50%. Now suppose that there are two identical merchants, A and B, who are both risk averse expected utility maximisers with utility of income given by u(y) = ln y. The income of each merchant will be 8 if their own ship returns and 2 if it sinks. As previously, the probability of a safe return is 50% for each ship. However, with probability p ≤ 1/2 both ships will return safely. With the same probability p both will sink. Finally, with the remaining probability, only one ship will return safely. (iv) Compute the increase in the utility of each merchant that they could achieve from pooling their incomes (as a function of p). How does the benefit of pooling depend on the probability p? Explain intuitively why this…
- Question 2: Assume that the risk-free rate, RF, is currently 8%, the market return, RM, is 12%, and asset A has a beta, of 1.10. (could be done on word document or excel). Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 2%, to be14%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A. From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?Question 17 Suppose Carole has a total wealth of $100,000 and a utility described by U = E -A She has a risk aversion coefficient of A-1. She can borrow and lend/invest at the risk-free rate of 2.8%. Suppose the optimal risky portfolio has an expected return of 12% and a standard deviation of 27.5%, What is her optimal amount to borrow or lend/invest at the risk free rate? Indicate investing/lending as a positive number and borrowing as a negative number. Round to the nearest cent ($0.01). Your answer should not include the $ sign. If your answer is $25.34, it should be written as 25.34. Question 18 Ayear ago, an investor bought 200 shares of a "no-load" mutual fund at $10.01 per share. No-load funds do not change "entry fees or "exit" fees when buying or redeeming shares. Sometime during the year, the fund paid dividends of $0.71 per share and the fund paid capital gains of $0.14 per share - and these payments were reinvested in the fund at an average price of $10.73 per share…Question 2 Ignore the term "maximum likelihood"
- Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesisQuestion 1 The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College Question 1 options: must be more than 22, since the population is always larger than the sample is 22 since the sample mean is an unbiased estimator of the population mean could be larger, smaller, or equal to 22 must be less than 22, since the sample is only a part of the population
- Problem 46 Hits at a website arrive at an average rate of 40 hits per hour according to a Poisson process. Let X denote the length in minutes from the time we start observing this website until the 1st hit is observedquestion 27 59% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 124 of the 243 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.05? The null and alternative hypotheses would be: Ho: p= (please enter a decimal) H1: p< (Please enter a decimal) 2.The test statistic _______ (please show your answer to 3 decimal places.) 3.The p-value = ______ (Please show your answer to 4 decimal places.)Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of discovering the disease in 97% of all afflicted individuals. Suppose further that when it is tried on healthy individuals, 5% of them are incorrectly diagnosed as having the disease. Finally, suppose that when it is tried on individuals who have certain other milder diseases, 10% of them are incorrectly diagnosed. It is known that the percentages of individuals of the three types being considered here in the populations at large are 1%, 96%, and 3%, respectively. Calculate the probability that an individual, selected at random from the population at large and tested for the rare disease, actually has the disease if the test indicates he is so afflicted.