Combinations of random variables

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Generate two random variables $X1$ and $X2$ from two independent normal distributions $N(-1, 2)$ and $N(8, 4)$ . Take $n = 10$ for both variables. Next, create a variable $Y = 5X1 - 3X2$ .

Calculate the mean and variance for the combined variable $Y$ by applying the theoretical equations for combining random variables and the values for the population parameters of $X1$ and $X2$ .

The theoretical mean of $Y$ is

The theoretical variance of $Y$ is

4. Probability Distributions: Practical 4

Combinations of random variables