I am given two random variables $X$ and $Y$, both are independent:
and X distributioN:
-2 -1 3
0.2 0.3 0.5
and Y distribution:
-1 0 2
0.2 0.4 0.4
I have to create distribution and then I have to calculate expected value and variance of $3X - 2Y$, $X^2 + Y^2$, $X \cdot Y$.
I do not understand how to create distribution of $3X - 2Y$, $X^2 + Y^2$ and $X \cdot Y$ accordingly. After creating distribution, I can calculate Expected value and variance, so I think I do not need any special formulas. However, I cannot understand how $3X - 2Y$ and others should be calculated.
Should I take "each $X$" and "each $Y$" and calculate $3X - 2Y$, so there would be 36 items? I do not really understand how this works and what is a meaning of $3X - 2Y$ if $X$ and $Y$ are two random indpendent variables.