Assume that a 25-year-old man has these probabilities of dying during the next five years: Age...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Assume that a 25-year-old man has these probabilities of dying during the next five years: Age at death Probability 25 I 0.00039 26 0.00044 27 0.00051 28 0.00057 29 0.00060 a) What is the probability that the man does not die in the next five years? (2 marks) b) An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next five years. The cost is $175 per year. So the insurance company will take in $875 from this policy if the man does not die within five years. If he does die, the company must pay $100,000. Let X denote the cash intake of the insurance company which depends on how many premiums the man paid. Find the distribution of X. (3 marks) Hint: if a 25-year-old man dies in the first year, the cash intake of the insurance company is -(100,000 -175)=-$99,825 under the policy; if he dies in the second year, the cash intake of the company is -(100,000 -2 175)= -$99,650 etc. If the man does not die within five years, the cash intake of the company is 5 175 = 875. c) What is the insurance company's mean cash intake? (2 marks) d) Suppose the insurance company insures one hundreds 25-year-old men under the terms of Question b). What is the probability that the insurance company will receive at least one claim? For simplicity, assume independence. (3 marks) Assume that a 25-year-old man has these probabilities of dying during the next five years: Age at death Probability 25 I 0.00039 26 0.00044 27 0.00051 28 0.00057 29 0.00060 a) What is the probability that the man does not die in the next five years? (2 marks) b) An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next five years. The cost is $175 per year. So the insurance company will take in $875 from this policy if the man does not die within five years. If he does die, the company must pay $100,000. Let X denote the cash intake of the insurance company which depends on how many premiums the man paid. Find the distribution of X. (3 marks) Hint: if a 25-year-old man dies in the first year, the cash intake of the insurance company is -(100,000 -175)=-$99,825 under the policy; if he dies in the second year, the cash intake of the company is -(100,000 -2 175)= -$99,650 etc. If the man does not die within five years, the cash intake of the company is 5 175 = 875. c) What is the insurance company's mean cash intake? (2 marks) d) Suppose the insurance company insures one hundreds 25-year-old men under the terms of Question b). What is the probability that the insurance company will receive at least one claim? For simplicity, assume independence. (3 marks)
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...
-
1. Hannah is applying for a life policy on her girlfriend Sarahs life. The policy is $500,000 and carries a large premium. Hannah is the main earner, so she is concerned about not being able to pay...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Social welfare is maximized when O Total social benefits have been maximized O total social costs have been minimized O total social costs equal total social benefits O marginal social costs equal...
-
A slit 0.240 mm wide is illuminated by parallel light rays of wavelength 540 nm. The diffraction pattern is observed on a screen that is 3.00 m from the slit. The intensity at the center of the...
-
A _______________ interval estimates the mean y-value for all individuals with a given x-value. In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
-
Argue the case for and against the political independence of central banks.
-
A lack of top management support has led to the downfall of many new systems projects during the implementation phase. Why is this support so important?
-
Walsh Company manufactures and sells one product. The following information pertains to each of the company's first two years of operations: Variable costs per unit: Manufacturing: Direct materials $...
-
Alan and Angel Young are both 36 years old. Mr. Young recently accepted a new job making $93,000 a year and Mrs. Young is currently unemployed. The Youngs have two children (ages 4 and 2), a dog, and...
-
The role of accountants in reporting and promoting sustainability includes: A. analysing of energy consumption costs B. reporting sustainability performance C. internal control procedures D. all of...
-
Revenue Cost of goods sold Gross margin Guatemala Ltd. Income Statement For the year ended December 31, 2022 Selling and admin expenses Wage expense Depreciation expense Interest expense Income...
-
Kirtland Corporation's accounting records showed the following at December 31: Transactions Beginning inventory, January 1 Units 480 Unit Cost $3.00 380 540 (240) 4.20 4.00 (780) Transactions during...
-
Frank is self - employed. In 2 0 2 3 , he had the following business meal expense: $ 2 , 0 0 0 spent for meals at restaurants with vendors and clients. How much of his meal expense can Frank deduct?...
-
With respect to the Ethernet frame: a . Show the frame format including the name, size ( in decimal ) , and the content ( in Hex ) of each field ( do not convert content to decimal or binary ) . ...
-
Write a Python and XML script to create an RPC server on Windows 11.
-
Suppose that you are given the following information. Total overhead is $ 6 0 , 0 0 0 . Of this, $ 4 0 , 0 0 0 is "machining," $ 1 0 , 0 0 0 is assembly." The machining cost pool is best driven by...
-
Akramin just graduated with a Master of Engineering in Manufacturing Engineering and landed a new job in Melaka with a starting salary of RM 4,000 per month. There are a number of things that he...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-6. On December 12, Irene purchased the building where her store is located. She paid...
-
During the 2012 tax year, Irma incurred the following expenses: Union dues..............................................................$275 Tax return preparation...
-
Cedar Corporation has an S corporation election in effect. During the 2012 calendar tax year, the corporation had ordinary taxable income of $200,000, and on January 15, 2012, the corporation paid...
-
Consider again Example 2. 8, where we have a normal model with improper prior \(g(\boldsymbol{\theta})\) \(=g\left(\mu, \sigma^{2} ight) \propto 1 / \sigma^{2}\). Show that the prior predictive pdf...
-
Assuming that \(\boldsymbol{X}_{1}, \ldots, \boldsymbol{X}_{n} \stackrel{\text { iid }}{\sim} f\), show that (2.48) holds and that \(\ell_{n}^{*}=-n \mathbb{E} \ln f(\boldsymbol{X})\).
-
Suppose that we have a total of \(m\) possible models with prior probabilities \(g(p), p=\) \(1, \ldots, m\). Show that the posterior probability of model \(g(p \mid \tau)\) can be expressed in terms...
Study smarter with the SolutionInn App