Easy -1.2 This is a straightforward application of standard results for expectation and variance of linear combinations of independent random variables. It requires only direct substitution into formulas E(aX+bY) = aE(X) + bE(Y) and Var(aX+bY) = a²Var(X) + b²Var(Y), with no problem-solving or conceptual insight needed—purely mechanical calculation.
2. The independent random variables \(X\) and \(Y\) are such that \(\mathrm { E } ( X ) = 20 , \mathrm { E } ( Y ) = 10\), \(\operatorname { Var } ( X ) = 5\) and \(\operatorname { Var } ( Y ) = 4\). Find:
a. \(\mathrm { E } ( 2 X - Y )\)
b. \(\operatorname { Var } ( 2 X - Y )\)
2. The independent random variables $X$ and $Y$ are such that $\mathrm { E } ( X ) = 20 , \mathrm { E } ( Y ) = 10$, $\operatorname { Var } ( X ) = 5$ and $\operatorname { Var } ( Y ) = 4$. Find:\\
a. $\mathrm { E } ( 2 X - Y )$\\
b. $\operatorname { Var } ( 2 X - Y )$\\
\hfill \mbox{\textit{SPS SPS FM Statistics 2020 Q2 [4]}}