You are Here: Home >< Maths

S3 statistics question =] watch

1. So my S3 book informs me that Var (X + Y) = Var(X) + Var(Y) (1)
and also that Var(aX) = (a^2)Var(X) (2)

But then let us supposed that Var(X) =5

Var(3X) = Var(X + X + X) = 5 + 5 + 5 = 15 from equation (1)
Var(3X) = (3^2)Var(X) = 9*5 = 45 from equation (2)

5 =/= 45

What have I done wrong?!

Cheers! xx
2. 3X is not equal to X + X + X.

Your first method would be correct if it were 3 observations of X.

Var(X1 + X2 + X3 ) = 3Var(X)

Actually that might not be right, but I'm pretty sure I'm right about why you're wrong...

I remember my teacher made a big deal about spotting whether or not a distribution was being multiplied (i.e. X -> 3X) or whether there were just multiple observations (i.e. X1 + X2 + ... + Xn).
3. (Original post by AnonyMatt)
3X is not equal to X + X + X.

Your first method would be correct if it were 3 observations of X.

Var(X1 + X2 + X3 ) = 3Var(X)

Actually that might not be right, but I'm pretty sure I'm right about why you're wrong...

I remember my teacher made a big deal about spotting whether or not a distribution was being multiplied (i.e. X -> 3X) or whether there were just multiple observations (i.e. X1 + X2 + ... + Xn).
Ahhh I see, so Var(3X) is like rolling a dice, multiplying the result by 3 and finding the variance and Var (X1 + X2 + X3) is like rolling 3 dice, adding the results together and finding the variance(?)

Cheers!
4. Yes. More generally, Var(A+B) = Var(A)+Var(B) is only true if A and B are independent (well, it just might happen to be true for some particular A and B that aren't independent, but you know what I mean).
5. (Original post by crrrrrash)
Ahhh I see, so Var(3X) is like rolling a dice, multiplying the result by 3 and finding the variance and Var (X1 + X2 + X3) is like rolling 3 dice, adding the results together and finding the variance(?)

Cheers!
Well I'm glad you could think of an example, I sure couldn't.

And DFanklin said yes so it must be true.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 31, 2010
Today on TSR

Results day under a month away

How are you feeling?

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants