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    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
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    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).
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    (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!
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    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).
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    (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. :p:

    And DFanklin said yes so it must be true. :p:
 
 
 
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