3.12 An investment firm offers its customers municipal bonds that mature after varyin of years. Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond, is Embedded LTI find a. P(T = 5); b. P(T > 3); c. P(1.4
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- A.) You wish to calculate the risk level of your portfolio based on its beta. The five stocks in the portfolio with their respective weights and betas are shown in the accompanying table A. Calculate the beta of your portfolio. (Format: 1.111) B.) Calculate the required rate of return for an asset that has a beta of 1.8, given a risk-free rate of 5% and a market return of 10% (Format: 1.11) *Not connected to the table*2.2 Consider a company that produces light bulbs. Its records show that the expected failuretime of a light bulb is 1500 h. To meet the current demand, the company is going toproduce 25,000 light bulbs. Assume an exponential probability distribution.(a) Determine the probability that a random light bulb lasts longer than t = 1000,1100, 1200, 1300, 1400, 1500, 1600, 1800, 2000, 2500, and 3000 h.(b) Graph the survival function versus time.(c) Determine the proportion of the 25,000 light bulbs that fail during the 13th hunderedhours.(d) Determine the proportion of light bulbs that fail during the 16th hundered hourgiven that they have survived 15 hundered hours.Suppose the incidence rate of influenza (flu) during the win-ter of 2008−2009 (i.e., from December 21, 2008, to March 20, 2009) was 50 events per 1000 person-months among students in high schools in a particular city. 14.32 A group of high-risk high school students was iden-tified in the winter of 2008−2009 who had 3+ previous episodes of influenza before December 21, 2008. There were 20 students in this group, each followed for 90 days, of whom 8 developed influenza. Test the hypothesis that the high-risk students had a higher incidence rate of influenza than the average high school student during the winter of 2008−2009. Report a one-tailed p-value. 14.33 Provide a two-sided 95% CI for incidence rate of flu among high-risk students during winter 2008−2009. Among 1200 students in one high school in the city, 200 developed a new case of influenza over the 90 days from December 21, 2009, to March 20, 2010. 14.34 What is the estimated incidence rate of flu in the 2009−2010 winter season…
- If customer interarrival times are exponentially distributed with rate 5 customers per hour, then O There is a 8.2% chance that a customer arrives within 5 minutes. There is a 81.8% chance that a customer arrives within 30 minutes. None of the answers are correct. There is a 34.1% chance that a customer arrives within 10 minutes. O There is a 71.3% chance that a customer arrives within 15 minutes.Q. 2 Suppose we followed a population of 175 persons for one year, and 50 had a disease of interest at the start of follow-up and another 25 new cases developed during the year. (a) What is the period prevalence for the year? (b) What is the point prevalence at the start of the period? (c) What is the cumulative incidence for the one-year period?Exercise 1. The annual number of murders in Chicago and LA are modeled as independent Poissons with means 500 and 240. [Note: The rates per 100,000 were about 23.8 and 7.3, resp, in 2016.] (a) What is the probability that Chicago sees over 525 murders next year [an increase of over 5%]? (b) What is the probability that LA sees over 252 murders next year [an increase of over 5%]? (c) What is the probability that Chicago and LA combined see a total of over 777 murders next year [an increase of over 5%]?
- John the barber rents a very small space that has room for 2 customers only. The time John spends on customers is exponentially distributed with an average time of 15 minutes. Potential costumers arrive in a Poisson manner at a rate of 3 per hour. What proportion of potential customers are admitted to John's shop?The time to failure of a certain type fo electrical component is assumed to follow an exponential distribution with a mean of 4 years. The manufacturer replaces free all components that fail while under guarantee. If the manufacturer wants to replace a maximum of 3% of the ocmponents, for how long should the manufacturer's stated guarantee on the component be?Assuming a loss frequency of a loss occurring once every 2 years and that the average value of losses that occur might be $40,000. Based on the above examples the expected loss is
- 71) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. What is the average length of the line? A) 3.429 B) 1.929 C) 1.143 D) 0.643 E) None of the above 72) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? A) 3.429 minutes B) 1.929 minutes C) 1.143 minutes D) 0.643…QUESTION 1 Calls come into a single help desk at an average rate of 5 per hour. On the average, the operator spends 10 minutes with each caller. Use basic queueing theory to answer the questions. What is the assumed distribution of the time between calls? Oa. Uniform distribution Ob. Exponential Distribution Oc. Normal Distribution d. General distribtion with know mean and sigma valueSuppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3% +0.7RM + еA RB = -2% + 1.2RM + eB OM = 20% ; R-squareд = 0.20; R-squareg = 0.12 What is the covariance between each stock and the market index? (Calculate using numbers in decimal form, not percentages. Do not round your intermediate calculations. Round your answers to 3 decimal places.) Stock A Stock B Covariance