Adding random variables

Imagine that we have two variables, x and y, which both have bell-curve
distributions about their respective averages.

If we know the averages, and their standard deviations, is it possible to
sum them and come up with a new average and standard deviation?

The general case, where the means and standard deviations are specified, but
the actual values are not.

You can get the mean by adding the two means. If they are
independent, you can get the variance by adding the two variances.

If X and Y are independent variable distributions:

E(aX + bY) = aE(X) + bE(Y) and
Var(aX + bY) = a^2Var(X) + b^2Var(Y)

a & b constants.

--
Greg

(remove BALL from address to reply)

Yes (given independence)

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1 14th November 19:51 anglewyrm External User Posts: 1	Adding random variables Imagine that we have two variables, x and y, which both have bell-curve distributions about their respective averages. If we know the averages, and their standard deviations, is it possible to sum them and come up with a new average and standard deviation? The general case, where the means and standard deviations are specified, but the actual values are not.

2 14th November 19:51 henry External User Posts: 1	Adding random variables You can get the mean by adding the two means. If they are independent, you can get the variance by adding the two variances.

3 14th November 19:51 greg External User Posts: 1	Adding random variables If X and Y are independent variable distributions: E(aX + bY) = aE(X) + bE(Y) and Var(aX + bY) = a^2Var(X) + b^2Var(Y) a & b constants. -- Greg (remove BALL from address to reply)

4 14th November 19:51 henry External User Posts: 1	Adding random variables Yes (given independence)