There is a 0.9986 probability that a randomly selected 29 -year-old male lives through the year. A life insurance company charge
1 answer:
Answer:
a) The value corresponding to surviving the year is -$176.
The value corresponding to not surviving the year is $109,824.
b) From the point of view of the insurance company, the expected value of the policy is $22.
As the expected value is positive, the company is expected to make profits from many such policies. According to the Law of large numbers, increasing the amount of policies, the deviation from the expected result will decrease. If the amount of policies is big enough, a profit is guaranteed for the company.
Step-by-step explanation:
a. From the perspective of the 29-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
The two events and the montery values for each are:
1) Surviving. The probability is 0.9986 and the monetary value is -$176.
2) Not surviving. The probability is (1-0.9986)=0.0014 and the monetary value is ($110,000-$176)=$109,824.
b. If the 29-year-old male purchases the policy, what is his expected value? Can the insurance company expect to make a profit from many such policies? Why?
The expected value can be calculated from the possible outcomes multiplied by its probabiltity of occurrence.
From the 29-year-old male, the expected value is:
The expected value for the company is the negative of the expected value of the client, so it has a expected value of $22 per person.
As the expected value is positive, the company is expected to make profits from many such policies. According to the Law of large numbers, increasing the amount of policies, the deviation from the expected result will decrease. If the amount of policies is big enough, a profit is guaranteed for the company.
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Answer:
(a) k'(0) = f'(0)g(0) + f(0)g'(0)
(b) m'(5) =
Step-by-step explanation:
(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e.,
this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>
on substituting the value x=0, we will get the value of k'(0)
{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}
(b) m(x) is a function of two functions f(x) and g(x) [ ]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows :
this will give <em></em>
on substituting the value x=5, we will get the value of m'(5).
{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}
{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }
{ NOTE : }