Standard deviation of a Random Variable (with respect to 3 other random variables)

expected valuerandom variablesstandard deviation

I have the following problem

Assume that you have three independent Random Variables X1, X2 and X3.
The expected value for each Random Variable is 3 and the standard deviation is 2.
Determine the standard deviation for the Random Variable Y = X1 – 5⋅X2 + 2⋅X3 + 4.
Hint: Variance[X] = V[X] = the square of the standard deviation = 22 = 4

I know how to do this for two variables (because there is a formula for this).
But how do I do this for three random variables?

Can someone please help me solve the problem or give me a hint.

Best Answer

Come on! the formula doesn't changes if you have 2 or 20 rv's.

$$\mathbb{V}[X_1-5X_2+2X_3+4]=\mathbb{V}[X_1]+25\mathbb{V}[X_2]+4\mathbb{V}[X_3]$$

this if, as is in your case, the rv's are independent (it is enough they are incorrelated)

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