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Chapter 6: Q.58 (page 381)

Life insurance If four 21-year-old men are insured, the insurer鈥檚 average income is

V=X1+X2+X3+X44=0.25X1+0.25X2+0.25X3+0.25X4

where Xiis the income from insuring one man. Assuming that the amount of income earned on individual policies is independent, find the mean and standard deviation of V. (If you compare with the results of Exercise 57, you should see that averaging over more insured individuals reduces risk.)

Short Answer

Expert verified

The mean and standard deviation,

渭V=303.35

蟽V=4853.79

Step by step solution

01

Given Information

Given in the question that the average income of the insures is

V=X1+X2+X3+X44=0.25X1+0.25X2+0.25X2+0.25X4

02

Calculate the mean and standard deviation of V

Let's compute the mean of V

Here,

渭x=303.35and蟽y=9707.57

Therefore,

渭Y=0.25渭X1+0.25渭X2+0.25渭X3+0.25渭X4=0.25脳303.35+0.25脳303.25+0.25脳303.25+0.25脳303.25=303.35

Compute the standard deviation ofV

蟽V=0.0625脳9707.572+0.0625脳9707.572+0.0625脳9707.572=23559228.83=4853.79

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