Let $X_1$ and $X_2$ be two independent random variables so that the variances of $X_1$ and $X_2$ are $x_1 = k$ and $x_2 = 2$, respectively. Given that the variance of $Y = 3X_2 - X_1$ is $25$, find $k$.
I have tried a lot but now finding the correct answer I think. I have got the answer as $19$ which is wrong.
Can anybody explain the process which I should follow to answer this Question?
Help is appreciated.
The following comes directly from the definition that $Var(aX+bY)=a^2Var(X)+b^2Var(Y)$
$$\begin{align*} Var(Y) &=Var(3X_2-X_1)\\\\ &=(3)^2Var(X_2)+(-1)^2Var(X_1)\\\\ &=9Var(X_2)+Var(X_1)\\\\ &=18+k \end{align*}$$
So $k$ must be $7$.