3. A company's cash position, currently at $3.7m, follows a generalized Wienerprocess falling on average $0.2m per quarter with volatility of $1.2m perquarter. With what probability does the company find itself with a nega-tive cash balance at the end of 5 quarters?(a) 0.3538(b) 0.1572(c) 0.2422(d) 0.9601(e) None of the above.

Answered: Image /qna-images/answer/1aabaf1f-d7fe-4698-80f3-81c207f6b3d0.jpg

Answered: 3. A company's cash position, currently…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 15 randomly selected pens yields no more than two defective pens. (b) Find the probability that this shipment is not accepted if 20% of the total shipment is defective. (Round your answer to three decimal places.)
7. An investment analyst has tracked a certain blue-chip stock for the past six months and found that on any given day it wither goes up a point or down a point. Furthermore, it went up on 25% of the days and down on 75%. What is the probability that at the close of trading four days from now, the price of the stock will be the same as it is today? Assume that the daily fluctuations are independent events
Suppose a life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old female for $300. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret the expected value of this policy to the insurance company.
a) Suppose that you have a job paying $50,000 per year. With a 15% probability, next year your wage will be reduced to $20,000 for the year. 1. What is your expected income next year? 11. Suppose that you could insure yourself against the risk of reduced consumption next year. What would the actuarially fair insurance premium be? b) It has been observed that the consumption expenditure of people drops when they begin their retirement life. This implies that their consumption is not smooth, and proves that they are not fully insured against leaving the workforce. Is this statement true? Explain. c) A water company owns water pipes that burst often due to poor maintenance. The company can invest GHS m in the maintenance of the pipes. More maintenance means less water loss through bursts, and less compensation payments to residents due to 1 flooding of their properties. Assume that the value of lost water is maintenance reduces the amount of loss. Assume that the value of damage to…
Consider a whole life insurance with annual premiums and a 20-year premium paying term issued to a select life aged 30, with sum insured $200,000 payable at the end of the year of death. (a) Write down an expression for the net future loss random variable. (b) Calculate the net annual premium.
Suppose a life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $170.According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544.Compute and interpret the expected value of this policy to the insurance company.
Suppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.
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%]?
A mortgage holding company has found that 0.09 of its mortgage holders default on their mortgage and lose the property. Furthermore, 0.93 of those who default are late on at least two monthly payments over the life of their mortgage as compared to 0.38 of those who do not default. What is the joint probability that a mortgagee has two or more late monthly payments and does not default on the mortgage? 0.3458 0.0342 0.0837 0.8463
The lengths of a particular animal's pregnancies are approximately normally distributed, with mean u = 260 days and standard deviation o = 8 days. (a) What proportion of pregnancies lasts more than 272 days? (b) What proportion of pregnancies lasts between 248 and 266 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 256 days? (d) A "very preterm" baby is one whose gestation period is less than 242 days. Are very preterm babies unusual?

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