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FinnZ [79.3K]
3 years ago
8

Suppose a life insurance company sells a $240,000 one year term life insurance policy to a 25-year old female for $210. The prob

ability that the female survives the year is .999592. Compute the expected value of this policy to the insurance company. I thought I would start with x value of 1 - 12, but I'm lost on what my P(X=x) value will be. I can do these when I'm shown a chart, however I'm lost when asked to do them from a story problem... An example would be appreciated. Thank you in advance
Mathematics
1 answer:
skelet666 [1.2K]3 years ago
5 0

Answer:

$112.08 every year.

Step-by-step explanation:

Let's suppose a game in which we bet a certain amount of money ''A'' to a certain result and the probability of that result is ''p''. If the prize that we get is ''P'' therefore the expected value of gain is  :

E=p(P-A)+(1-p)(-A)=pP-A

Now,let's suppose that the female is ''betting on her death'' ⇒

P(she survives) = 0.999592

P(she doesn't survive) = 1 - 0.999592=4.08(10^{-4})

E(25-year old female) = 4.08(10^{-4}).(240000)-210=-112.08

The negative sign of E is important.It means that every year the 25-year old female will lose $112.08.

Therefore, the expected value of this policy to the insurance company is $112.08 every year.

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