Having a lot of trouble with a particular problem in the topic of variance. The problem is:(adsbygoogle = window.adsbygoogle || []).push({});

"Suppose you are organizing a game where you charge players $2 to roll two dice and then you pay them the difference in scores. What is the variance in your profit from each game? If you are playing a game in which you have positive expected winnings, would you prefer a small or large variance in the winnings?"

I already calculated the variance (more details of the problem were not mentioned b/c I already calculated the variance) and it was around 2.06 and the expected value (mean) is 1.94. I would guess a larger variance because then you can take a chance at trying to get higher values while knowing that you have a good chance of getting a positive income in the end. But I keep second-guesing myself of that and I am just not sure, lol.

Also, having a lot of trouble with linear combinations. For example, I have a problem like this:

Suppose that the random variable X has a probability density function of f(x) = 2x for 0 <= x <= 1. Find the PDF and the expectation of the random variable Y in the following cases:

a. Y = X^3

There are 3 more parts but I can do those myself if I can just figure out how to do one. I just have no idea where to start. I read the book and the notes and still having trouble figuring out what to do here. I guess I need to say for example:

f(x^3) = (2x)^3 = 8x^2 would be the new PDF?

and ...

E(x^3) = (E(x))^3 = ... ?

I don't even know what I am doing ... lol.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Statistics -> Variance and Linear Combinations

**Physics Forums | Science Articles, Homework Help, Discussion**