Random Variable X

#1
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
#2
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.
 
#3
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
#4
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.

Start with just the mean.
 

Dragan

Super Moderator
#8
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]
 

Dragan

Super Moderator
#12
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.