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
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)

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[4]=0