An insurance policy on an electrical device pays a benefit of $2850 if the device fails...

An insurance policy on an electrical device pays a benefit of $2850 if the device fails during the first year. The amount of the benefit decreases by $950 each successive year until it reaches 0 . If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.29.

Find the expected benefit under this policy?

Solutions

Expert Solution

Let x : be the benefit amount

The probability of failure during that year is 0.29

The probability of success = 1 - 0.29 = 0.71

The probability that the device fails in the first year is

Benefit amount on the first year is $2850

The probability that the device fails in the second year is

Benefit amount on the second year is $2850-$950 = $1900

The probability that the device fails in the third year is

Benefit amount on the third year is $1900-$950 = $950

x	2850	1900	950
P(x)	0.29	0.2059	0.146189

The formula for Expected value is ,

The expected benefit under this policy is $1356.59

If you round this to nearest whole number, it would be $1357 .

orchestra answered 1 year ago

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