I just had a tricky question about calculation of expectation of a variable. So, we have a pack of $52$ cards and $X_1\cdots X_{50}$ are outcomes of first $50$ draws. Each $X$ can take values from $1-52$ If we have a variable $A = X_1- 2X_2 + 3X_3$, how do we calculate expectation of $X$? I tried thinking hard but the fact that $A$ is combination of $3$ variables, each having $52$ outcomes and me not have learned expression of one random variable in terms of others is making the job really difficult.
So, how do we solve this kind of a question?
The expected value of all the $X_i$ is $\frac{53}2$ since all of $1,\dots,52$ are equally likely to be drawn, so that of $X_1-2X_2+3X_3$ equals that of $X_1-2X_1+3X_1$, i.e. the answer is $2X_1=53$.