Probability Help

[Raknarg]

I'm hoping someone here understands statistics pretty well.. I've seen this come up a few times:

E (3X + 1)
Var (3X + 1)

That's expected value and variance. But I have no idea what i'm supposed to do with those transformations to x, or what it means. Anyone know?

[DemonWasp]

Expected value and variance have properties that will let you manipulate them. See:
http://en.wikipedia.org/wiki/Expected_value#Properties
http://en.wikipedia.org/wiki/Variance#Properties

In your example, because E ( X + c ) for c some constant is E ( X ) + c, we know that E ( 3X + 1 ) = E ( 3X ) + 1.

Similarly, we know that E ( aX ), for some constant a, is a * E ( X ), so E ( 3X + 1 ) = 3 * E ( X ) + 1.

The rules for variance are different, but similar. You should find that Var ( 3X + 1 ) = 9 * Var ( X ), if I'm doing it correctly.

[Raknarg]

Wat's the point, is it to scale between different sample sizes?

[Tony]

The point is that if you know the distributions for a given random variable (X in your examples), you could figure out the expected outcomes of more complex systems.

If I propose a bet where you flip a coin 3 times and get paid $1 + $1 for each heads. How much would you expect to win? E (3X + 1) where X depends on the fairness of the coin.

[Raknarg]

Ohhh that makes sense.