Question

A random variable X has a mean of 10 and a standard deviation of 3. A random variable Y has a mean of 15 and a standard deviation of 4. What is the standard deviation of the combined random variable X+Y?

Answer 1

Assuming X & Y are INDEPENDENT random variables, then:
var( X + Y ) = var(X) + var(Y)
Thus, the var(X+Y) = 9 + 16
= 25
And, as a result (taking the square root of the variance), the standard deviation of "X+Y" is equal to 5.
Does this help?

Answer 2

Yes thank you!

Answer 3

The important thing to remember is that when dealing with INDEPENDENT random variables, their variances are additive. Thus, to calculate their standard deviation you have to:
1.) Square the two standard deviations
2.) Add the results together
3.) Then take the square root of the variance.