# Random Variable X

#### iain08

##### New Member
So this question is on my practice final, and the professor provided the work for how to solve it and I cannot figure it out.

Suppose that the random variable X has a mean u = 5 and standard deviation o=8. The mean and standard deviation of Y=2X-4 is?

The answer is 6 and 16, respectfully, and I do not know how to get there. Anybody willing to help me out?

#### Dragan

##### Super Moderator
So this question is on my practice final, and the professor provided the work for how to solve it and I cannot figure it out.

Suppose that the random variable X has a mean u = 5 and standard deviation o=8. The mean and standard deviation of Y=2X-4 is?

The answer is 6 and 16, respectfully, and I do not know how to get there. Anybody willing to help me out?

Your professor should have covered the properties of the Expectation Operator i.e. E[X]. If you understood these properties, then the answers to your question should be straight-forward to you.

#### iain08

##### New Member
Well we did that, but the data was given by a chart that had both X and Y and their probabilities at each number and we found out everthing from there. So normally I would take the Covariance of X and Y and subtract the product of the two means from that.

#### Dragan

##### Super Moderator
Well we did that, but the data was given by a chart that had both X and Y and their probabilities at each number and we found out everthing from there. So normally I would take the Covariance of X and Y and subtract the product of the two means from that.
You're thinking "too hard". Why do you need the Covariance between X and Y?...based on the question you posed.

#### iain08

##### New Member
To show how X and Y change together right? Which I guess is what y=2x-4.

#### Dragan

##### Super Moderator
No, Hint: E[Y] = 2*E[X]-4.

Do you see?

#### iain08

##### New Member
So if I plug in 5 as x I get y=6. But to get the 16?

#### Dragan

##### Super Moderator
Okay, fine, we're getting somewhere.

Now, look in your notes for the properties of Variance [Var]. e.g. If Y = a*X, then Var[Y] = a^2*Var[X]

#### iain08

##### New Member
Well I have Var(X + Y) = Var(X) + Var(Y)

and

Var(X+Y) = 2Cov(X,Y)

#### Dragan

##### Super Moderator
There is no Var[X + Y] here. It's just the Var[Y]= ?

#### iain08

##### New Member
I can't find anything in my notes about just Var[Y]. Except that Cov(X,Y) = Cov(X, X^2).

#### Dragan

##### Super Moderator
What's the Variance of X ---you're given that the standard deviation of X=8 . Then look up at my previous post (#9) and apply the formula.

#### iain08

##### New Member
Well I plugged in some numbers into a formula and got 4(64) = o^2, so o=16.

#### Dragan

##### Super Moderator
I think you have it....remember that the Variance of a constant is zero...i.e. don't leave out the fact that Var=0