###### A Life Insurance Company Sells a Term Insurance Policy to males aged 21 who will pay $100,000 if the insured dies in the next five years. The chance that a randomly selected male will die every year is reflected in mortality tables.

###### The insurance company receives a fee of $250 annually to pay in exchange for insurance. The amount of Y the business earns based on a randomly selected policy such as this is $250 annually, less the $100,000 it will have to pay if the insured passes away. Below is the distribution of probabilities for the Y number:

## (A)

###### Give the reason why your company incurs an expense of $98,750 from the policy if the insured dies before the age of 25.

## (B)

###### Find the anticipated value for Y. Explain the significance of this figure for the insurance firm.

## (C)

###### Determine the average deviation for Y. Discuss the implications of this result for the insurance company.

## A Life Insurance Company Sells a Term Insurance Policy

###### The presentation will focus on: “**A life insurance company sells a term insurance policy** to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The probability. “– Transcript of the presentation:

1. A life insurance company offers a period insurance plan to a 21-year-old male who pays $100,000 if the insured dies in the next 5 years. The chance that a randomly chosen male will die every year is reflected in mortality tables.

The insurance company pays a premium of $250 per year to pay for the insurance. The amount X that a company receives from the policy amounts to $250 annually less the $100,000 it is required to pay if the insured passes away. Below is the spread of the amount X. Fill in the gaps in the table, and then calculate the mean profit, mx.

### Age

21 22 23 24 25

>=26

Profit

-$99,750

-$99,500

-$99,250

-$99,000

-$98,750

$1250

Prob.

.00183

.00186

.00189

.00191

.00193

**2.** Section 6.2 Second Day Rules for Means and Variances

**3.** The Law of Large Numbers This is crucial! The law states that

The more samples we have the more similar the mean will be to what should or “should” be.

**4.** The Rules of Means

If X and Y are both random variables and A and B are fixed numbers Then

We’ll go over these separately in just a few minutes…

**5.** Simply put

If you’re looking to find the mean value of the sum or difference between two variables randomly, just need to subtract or add their respective means.

If the average for X is 1500, and the mean of 1000 is Y, then the mean of X plus Y =

**6.** The second rule

It means that if you add an amount, such as a in each sample, we will add a to our average.

If we also add every value in the test by b, then we need to multiply the average by b.

## 7. Rules for Means Explicitly Demonstrated

The X symbol represents units sold to the military division

1000

3000

5000

10,000

Probability

0.1

0.3

0.4

0.2

Y = units that are sold to a civilian division

300

500

750

Probability

0.4

0.5

0.1

If the company earns $2000 for every military unit sold, and $3500 for each civilian item sold calculate the average profit.

**8.** Rule of Variance

If X is an unknown variable and a and b are fixed numbers If X is a fixed number, then …

And If we add the exact number of a to everything in our sample it won’t alter the variation. If we multiply each number by b, your standard deviation will be multiplied by b thus it is divided by the square of b.

**9.** What happens if they’re separate?

If the two are not related that is, they do not have any effect on each other, so ….

The r value is 0 which means…

## 10. Examples…

If both X and Y are random variables that are not independent, and…

## 11. Another example:

Let’s say that Tom’s score from the course of golf is X, the random variable, and George’s score during a round of golf is a random variable named Y. Let us assume that their scores are independent.

Find their average combined scores as well as how much they differ from their scores, if applicable.

## 12. More details…

One of the techniques you will need to master in this area is to combine two random variables that are independent and determining probabilities.

Find the mean, combined with the standard deviation. Then, tackle the problem in the same way just like the normal curve probabilities (find your Z-score).

In a fair game,

## 13. Example

Return to Tom and George’s golf match. What percentage of the time could we anticipate Tom to be victorious?

Tom: = =10

George: = = 8

(x-y) = 10

(x-y) = 12.8

## 14. Homework

Chapter 6

#37, 38, 42, 44, 47, 48, 56

## 15. Things to be studying to pass your test

How can you test for independence?

Slides 17 and 16 of Chapter 6 Day 2 of Day 2.

Calculating the mean and std. deviation from the distribution

Law of Large Numbers

How do you define std and mean? deviations are affected by addition and multiplication

Review Sheet