7.3 Combining and Transforming Random Variables

3 practice questionsNot yet reviewed

Notes

$E(aX + b) = aE(X) + b$.
$E(X + Y) = E(X) + E(Y)$, always.
$\text{SD}(aX + b) = |a|\,\text{SD}(X)$.
For independent $X$ and $Y$, variances add: $\text{Var}(X + Y) = \text{Var}(X) + \text{Var}(Y)$. Standard deviations do not add.
Example: If $E(X) = 5$ and $Y = 3X + 2$, then $E(Y) = 3(5) + 2 = 17$.

$E(X) = 5$ and $Y = 3X + 2$. What is $E(Y)$?

A student's morning routine takes an average of 12 minutes to get ready ($X$) and 8 minutes to commute ($Y$). The expected total time $E(X + Y)$ is:

$X$ and $Y$ are independent with standard deviations 3 and 4. What is the standard deviation of $X + Y$?