Statistics

Factual Questions
1

I have a statistical question that I know I should be able to answer myself, but I can’t. Here it is.

Let’s say I have several independent variables, each with a known normal distribution; i.e., I know the mean and standard deviation of each variable. How I calculate the standard deviation of the sum of the variables?

Let me use an example to illustrate. Suppose I am going to put three electrical resistors in series. The first resistor comes from a box of resistors that has a mean value of 10 ohms and a standard deviation of 1 ohm. The second resistor comes from a box that has a mean of 20 ohms and a standard deviation of 2 ohms. The third resistor comes from a box that has a mean of 30 ohms and a standard deviation of 3 ohms. By picking one resistor at random from each box and putting them in series I know that, if I do this many times, the mean value of the resistance I get will be 60 ohms (10+20+30), but will be the standard deviation around that mean?

2

It’s the square root of the sum of the squares. In your example, it’d be

sqrt(1^2 + 2^2 + 3^2)= sqrt(1+4+9) = sqrt(14) Ohms

3

Aha. THAT’s what it was. Thanks, Tim.