So, this Monday I have an Actuarial Exam. This is the first of a series of 10 tests, and deals with probability. It is affectionately called the P-Test. This wonderful test costs $175 to take, and about 1 in 3 who take the test pass it on their first try. In other words, P(pass) = 0.333 .
If that doesn't tell you how hard the test is, here's an example from the study guide.
77. A device runs until either of two components fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is
f (x, y) = (x + y)/8 for 0< x <2 and 0< y <2.
What is the probability that the device fails during its first hour of operation?
(A) 0.125
(B) 0.141
(C) 0.391
(D) 0.625
(E) 0.875
I'll give you a hint--it's the blue one. If any of you can tell me why, you're doing better than I did!
So, if any of you want to say a little prayer for me, that'd be GREAT!
2 comments:
I'm not sure which of us has the hardest job today, you with your crazy test, or me caring for a 2 year old and 2 month old all day.
:)
I'll be praying for you.
well, from what I can see, .625 is 5/8 and (2+2)/8 = 4/8 which would be the maximum life expectancy. Obviously if the objects have an equal chance of failing, then it is likely that one of them will fail in less than one hour, which means the likely hood that the device fails in the first hour is better than 50%. But 7/8 is way too high as at that rate the devices would have to fail on average at about 40 minutes instead of one hour. Thus, the answer must be the 62.5%
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