[SamAdams76]

These tests are not easy. Here is a sample question:

The lifetime of a printer costing $200 is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, a one-half refund if it fails during the second year, and no refund for failure after the second year. Calculate the expected total amount of refunds from the sale of 100 printers.

• (A) $6,321
• (B) $7,358
• (C) $7,869
• (D) $10,256
• (E) $12,642

[meyer]

A lot of it has to do with building the appropriate equation out of the information given. The first sentence in the example brings a question to my mind - “exponentially distributed with a mean of 2 years...” I can figure out a mean of 2 years, but the exponentially distributed would give me pause.

I suppose that if you’re in the field, there’s a typical standard exponential distribution (like a bell curve and standard deviations and all that), and one would know that just as my mother knew the difference between a peck of strawberries and a quart of strawberries.

[CheshireTheCat]

I’m going to pick B. They say that when you don’t know the answer, you should pick C and you have a greater chance of getting right answer than any other letter choice.

But in my experience, B more often turned out to be the right answer.

[kosciusko51]

The answer is D.

[TexasGator]

“with mean 2 years. “

with a mean life of 2 years?

[DoodleBob]

The answer is the sum of $200 * the probability of the printer failing during the first year and $100 * the probability of the printer failing during the second year, multiplied by 100.

The probability of X in the exponential distribution is L * exp (-L*X), where the average = 1 / L. In this problem, L = 0.5.

Thus, the first probability is 0.5 * exp (-(0.5*1)) = 0.3033 and the second probability is 0.5 * exp (-(0.5*2)) = 0.1839.

The first expected payoff is 0.3033*$200 or $60.65 and the second payoff is 0.1839*$100 or $18.39.

The sum of the payoffs is $79.04. That payoff for 100 printers is $7,904.

Since I'm (clearly) not an actuary, I'll round to the closest and guess C.

[Neanderthal]

"The lifetime of a printer costing $200 is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, a one-half refund if it fails during the second year, and no refund for failure after the second year. Calculate the expected total amount of refunds from the sale of 100 printers.

(A) $6,321
(B) $7,358
(C) $7,869
(D) $10,256
(E) $12,642

The answer is (D).

F(1) = .393
F(2) = .632

So (0.393 x $200) + (0.632 - 0.393) x 100 = $102.50 refund per printer.

Times 100 printers = $10,250.

I am an actuary, by the way, so I will be very embarrassed if I made a mistake here.