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View Full Version : IDENTICAL? No so much.

joni308
07-23-2011, 12:14 AM
Turns out every time I'm wrong on a problem it's the problem itself is wrong.

http://actuaries4u.ning.com/forum/topics/not-happy-with-what-i-see-why

JdPActuary
07-23-2011, 09:50 AM
They assigned a single random variable (Y) to the cost of running one of the two machines. There is no Y1 and Y2. Just Y. Contrary to your argument this does in fact imply that the machines behave identically (at least as far as the cost of running them goes).

An easy problem to misinterpret though. Can anyone confirm/deny that my explaination is correct?

joni308
07-23-2011, 11:18 AM
They assigned a single random variable (Y) to the cost of running one of the two machines. There is no Y1 and Y2. Just Y. Contrary to your argument this does in fact imply that the machines behave identically (at least as far as the cost of running them goes).

An easy problem to misinterpret though. Can anyone confirm/deny that my explanation is correct?

It explicitly says 'TWO MACHINES'.

What else do you want? To write it down for you? Y1 and Y2? When you have a real world problem and your client tells you I have 2 machines (they are both the same, the model HP 45T324) it this how you'll interpret it? 2Y?

My question is do you even understand what 2Y means? Please try to.

In real world there are no 2 things that a priori behave the same. Had there been any, then that behavior would not be random but rather deterministic.

By the way, if you are smart enough, like myself, you can spot the problem is wrong and still solve it right if it's in the exam. With the information provided I can understand immediately that they expect you to solve it wrong so go along. Do solve it wrong and get the points.

And I'm not presenting this problem here so I get others confirmation that it's indeed the case. I'm just warning you that you need to have your eyes open out there. There is nothing flawless out there. Not your textbook, not your professor nothing. So don't treat anything as such.

JdPActuary
07-23-2011, 12:00 PM
What else do you want? To write it down for you? Y1 and Y2? When you have a real world problem and your client tells you I have 2 machines (they are both the same, the model HP 45T324) it this how you'll interpret it? 2Y?

My question is do you even understand what 2Y means? Please try to.

Actually, yes. They tell me that the cost of running one of the machines is Y. I have two machines. Therefore it will cost me 2Y to run two of them.

If they told me that the cost of running either of the two machines is identically distributed with variance 3.5, then I would have to treat them as separate variables. That's a different situation though.

It's tough to think of a specific real life example of this kind of situation, but sometimes you need to suspend your disbelief so to speak and just deal with the information the problem gives you.

joni308
07-23-2011, 12:14 PM
Actually, yes. They tell me that the cost of running one of the machines is Y. I have two machines. Therefore it will cost me 2Y to run two of them.

If they told me that the cost of running either of the two machines is identically distributed with variance 3.5, then I would have to treat them as separate variables. That's a different situation though.

It's tough to think of a specific real life example of this kind of situation, but sometimes you need to suspend your disbelief so to speak and just deal with the information the problem gives you.

I'm sorry my friend but this is excruciating. If one machine has an expense of Y then having 2 machines has an expense of 2Y? That would of course be true if the expense was predetermined such as fixed maintenance cost 6 months after purchase.

1. Do you understand that Y is a random variable?
2. If yes, do you know what a random variable is?

The expense for machine 1 would be one observation from this r.v and the expense for the other would be another. Or to be correct the expense for machine 1 is a rv from this distribution and the expense for the other another rv from the same distribution.

JdPActuary
07-23-2011, 12:34 PM
I very much understand what a random variable is. What I'm saying is that this is the way the problem is worded: the cost of machine 1 is a random variable Y, and the cost of machine 2 is the same random variable Y. They are not different. Show me where it says that they are in the problem. You've already admitted yourself that it says no such thing.

Regardless, I don't think we're going to convince eachother of anything here. I'm interested to see if anyone else has an opinion on the wording of this problem (which I admit could be better).

Kaner3339
07-23-2011, 12:57 PM
Two cell phones plucked off of an assembly line aren't guaranteed to fail at identical moments in time. I think they require separate observations.

joni308
07-23-2011, 01:12 PM
go and buy 2 exact same computers from BestBuy. Sit them on your desk and have them do the exact same work. Each could break and require repair. Randomly. You are telling us they will break identically.

This is exactly what the problem says. 2 identical computers. The problem is presenting to you a very realistic, out of life scenario. In fact now on my desk I have 3 IDENTICAL monitors. All 3 Turned on all the time. Bought at the exact same time. One of them broke in 9 months and I got a replacement. The other 2 are still going strong.

the_integral_actuary
07-23-2011, 01:23 PM
They assigned a single random variable (Y) to the cost of running one of the two machines. There is no Y1 and Y2. Just Y. Contrary to your argument this does in fact imply that the machines behave identically (at least as far as the cost of running them goes).

An easy problem to misinterpret though. Can anyone confirm/deny that my explaination is correct?

I think you are right. They assigned one random variable to model the cost for both.

the_integral_actuary
07-23-2011, 01:23 PM
go and buy 2 exact same computers from BestBuy. Sit them on your desk and have them do the exact same work. Each could break and require repair. Randomly. You are telling us they will break identically.

This is exactly what the problem says. 2 identical computers. The problem is presenting to you a very realistic, out of life scenario. In fact now on my desk I have 3 IDENTICAL monitors. All 3 Turned on all the time. Bought at the exact same time. One of them broke in 9 months and I got a replacement. The other 2 are still going strong.

Even though it may not be realistic, they used a single random variable to model the cost for both. That is what is given in the problem...

JdPActuary
07-23-2011, 01:25 PM
I can't think of another way to explain this where I won't be repeating what I've already said. All I can say is that you guys are trying too hard to rationalize this problem and make sense of it in real life when you need to just deal with what the problem gives you.

JdPActuary
07-23-2011, 01:26 PM
I think you are right. They assigned one random variable to model the cost for both.

Thank you!! I was starting to feel alone!

joni308
07-23-2011, 01:27 PM
I very much understand what a random variable is. What I'm saying is that this is the way the problem is worded: the cost of machine 1 is a random variable Y, and the cost of machine 2 is the same random variable Y. They are not different. Show me where it says that they are in the problem. You've already admitted yourself that it says no such thing.

Regardless, I don't think we're going to convince eachother of anything here. I'm interested to see if anyone else has an opinion on the wording of this problem (which I admit could be better).

Yo don't know how to convince. If I were you I would provide an example at least to shut me up. So I'll do all the work for you. You see, I'm on your side. You are not.

2 identical air conditioners, that work simultaneously in the same room, will require a filter replacement every 3 months. The cost is a random variable as the cost of the filter and labor cost change constantly and not in a predictable way. Then YES, the cost of maintenance, and that alone, is 2Y.

But this is never the case. The problem talks about the total expenses of running the 2 machines. And if you were to just like that omit the unexpected costs then why bother do the analysis in the first place? It's exactly like I try to apply complicated math models to hedge my position in MCD and hire highly paid PhDs to do that for me (MCD is a low beta stock) while in fact 97% of my money is in a small cap stock, that swings 15% a day up and down, totally unhedged.

Kaner3339
07-23-2011, 01:32 PM
so the problem is wrong

JdPActuary
07-23-2011, 05:19 PM
Yo don't know how to convince. If I were you I would provide an example at least to shut me up. So I'll do all the work for you. You see, I'm on your side. You are not.

2 identical air conditioners, that work simultaneously in the same room, will require a filter replacement every 3 months. The cost is a random variable as the cost of the filter and labor cost change constantly and not in a predictable way. Then YES, the cost of maintenance, and that alone, is 2Y.

A very good real life example actually. Maybe they're trying to model only the "expected" maintenance costs as you put it. Maybe air conditioners are exactly the type of machine they're modeling with the random variable Y. In the end, who cares? The problem gives you the information. Personally, I'm not going to put this much thought into a problem when I'm taking P. I'm just gonna do it and move on.

Gandalf
07-23-2011, 06:42 PM
If you encountered this exact wording on Exam P (exam wording is likely to be clearer) I think you would be wise to interpret it as X+Y1+Y2. FWIW, which may be exactly what you paid for it.