# In general, is it easier to solve problems that have random variables, or problems that are basically the same that don't [closed]

This question is asked because I don't understand how random variables will affect various math problems, and knowledgeable mathematicians would.

By easier, we mean less steps

• If we make our own problems, random variables are wholly optional. Why? Because if we wanted random variables in a non-random variable problem, we just add a random source to the example problem. Having a random source automatically makes the variables into "random variables" for a problem.
• The variables being random variables or not doesn't seen to make any difference to certain example problems

A quick concrete example --
You have a bunch of range of numbers (like $33$ to $77$), which represents your IQ,
each with a corresponding percentage which represents your chance of getting cancer. That is what is inside one set.

There are many sets and each set has different continuous numbers and percentage

You find a comparative trend to solve this.

This example can be made random just by having the IQ number be randomly generated instead of already given. Now you have random variables. But these random variables don't seem to really affect the problem or example at all .

Beacause all we care about is the trend between the number and percents, and how they relate to the other numbers and percent in the other sets.

Here's another example where you can easily make the problem have random variables or not -- what math topic is this kind of example part of? or what is needed to understand how to solve it?, but I think the problem is fundamentally different from the IQ example.

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Could you give an example of what you mean? It is hard to read a question about facts out of this ... –  Hagen von Eitzen Sep 29 '12 at 11:24
Do you really mean random variable or are you talking about creating word problems by picking numbers in a special way so that certain quantities exactly cancel out vs. picking numbers less deliberately? –  binn Sep 29 '12 at 13:04
@high are you confused by the fact that there is nothing random about a random variable ? (i.e. it s just a specific kind of function). What definition are you using when you talk about a "random variable" ? –  Beltrame Sep 29 '12 at 17:09
the definition of a random var im using is "if the source or the outcome is random, then you have random variables." -- yes i mean random variables -- stats.stackexchange.com/questions/38247/does-anyone-know-what-exactly-is-a-rando‌​m-variable –  kittensatplay Sep 30 '12 at 23:40
a concrete example that i made is stats.stackexchange.com/questions/38235/formula-for-a-comparative-trend-any-of-t‌​hese-http-stattrek-com-statistics –  kittensatplay Sep 30 '12 at 23:43
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## closed as not constructive by Hagen von Eitzen, whuber, Michael Greinecker♦, Qiaochu YuanOct 7 '12 at 4:06

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## 1 Answer

The question is really too vague to answer in any precise sense. Of course, it will depend on what kind of problems you are considering. But note also that introducing random variables will change what kind of questions that you can ask. You cannot expect to find exact answers, but have to be satisfied with the probability of something happening, or what happpens "on average". When you ask different questions, there is no way to tell if they are easier or not.

If you want to describe something in the real world, models will often be simpler to analyze without random variables, but they can be more realistic when you allow for uncertainty. Take away the randomness from multivariate linear regression, and you are left with linear algebra. Take away the randomness from discrete time series, and you are left with difference equations. In both cases, the deterministic case is something you need to understand before you tackle the stochastic case.

In some cases allowing for randomness can simplify the analysis. We cannot predict the weather in detail, but can get good results on average. We do not know if the solar system is stable, but can say that with point sized masses and random initial configuration, the probability of a collision at some future time is zero. We have simple questions about the primes that we do not know the answer to, but stochastic objects with behavior similar to the primes are better understood. In these cases we know what happens on average, but we do not know if the one "real" case that we actually have belongs to the "typical" cases, or whether it is some freak case with completely uncharacteristic behavior.

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that's why the question says in general, it never asks for any precise anwsers. "When you ask different questions, there is no way to tell if they are easier or not." -- but it we're not asking different questions, we're asking if it's easier based on equalivilivent questions, "or problems that are basically the same" as stated clearly in the title –  kittensatplay Sep 30 '12 at 23:47
helpful -- "If you want to describe something in the real world, models will often be simpler to analyze without random variables" –  kittensatplay Sep 30 '12 at 23:50
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