# Adding Independent Random Variables Given Their Individual Expectations and Variance

How do I add or subtract independent random variables (R.Vs) when given their individual expectations and variance? I'm a student in high school and I haven't covered distributions yet, so please try not to use them.

Example, R.Vs A, B & C

Where

$$E(A)= 35\;\;\ Var(A)=8\\ E(B) = 25\;\;\;\; Var(B)=9\\$$

Calculate the expectation and variance of:

$$A + 2B$$

Let $$A$$ and $$B$$ be two random variables and $$c$$ be a constant. Then,
1. $$\mathbb{E}[A + cB] = \mathbb{E}[A] + c\mathbb{E}[B]$$ and
2. $$\operatorname{Var}(A + cB) = \operatorname{Var}(A) + c^2 \operatorname{Var}(B)$$ (assuming $$A$$ and $$B$$ are independent).
Variance is defined in terms of the expectation. In particular, $$\operatorname{Var}(X) = \mathbb{E}[(X - \mathbb{E}[X])^2]$$. See if you can use this definition to prove property (2) from property (1).