Hi,
Thanks for your reply, but I am still unsure by your last few sentence.
shouldn't Var(Y) = Var(20X) = 400Var(X)?
Whoops! I think I confused myself there
Apologies, please ignore that last sentence (actually, you can probably ignore that entire comment
) I've written something that may have confused you (and myself).
Let's start again:
The question states that the batteries are
independent of each other.
So, Y = X
1 + X
2 + ... + X
20 Note, Y = 20X is NOT true, each 'X' is independent of the next (
this is where I went wrong last time).
Recall that for independent variables A and B,
Var(A + B) = Var(A) + Var(B)
i.e. we add the individual variances together
Therefore,
Var(Y) = Var(X
1 + X
2 + ... + X
20) = Var(X
1) + Var(X
2) + .... + Var(X
20).
We are adding the individual variances together.
Note the difference between the above, and Var(Y) = Var(20X). In the above, we are adding each individual variances together, which is why we multiply the variance by 20.
I hope this clears things up for you, and apologies for any confusion