Please do the following questions with full handwritten working out.Mean= 0.177911Variance=0.057632 1. Let x = 40, 8 = 0.07 and assume mortality follows DeMoivre's Law with amaximum ageof 120. Determine the expected value and variance of the randomvariable Z40 for a whole life policy on this individual.2. Suppose now that 500 individuals of the type in question 1 buy insurance with abenefit of $250,000. Find the amount of money the insurer will need to hold to be95% certain that the company will be able to pay the benefits to these individuals.

Given, mortality follows DeMoivre's Law with a maximum age of 120Age, force of interest,

Answered: 1. Let x = 40, 8=0.07 and assume…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please do the following questions with full handwritten working out.

Mean= 0.177911

Variance=0.057632

1. Let x = 40, 8 = 0.07 and assume mortality follows DeMoivre's Law with a
maximum age
of 120. Determine the expected value and variance of the random
variable Z40 for a whole life policy on this individual.
2. Suppose now that 500 individuals of the type in question 1 buy insurance with a
benefit of $250,000. Find the amount of money the insurer will need to hold to be
95% certain that the company will be able to pay the benefits to these individuals.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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