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Consider the following two independent random variables, $\displaystyle {X}$ and $\displaystyle {Y}$ .

Random variable $\displaystyle {X}$ has a mean of 23 and a standard deviation 10.

Random variable $\displaystyle {Y}$ has a mean of 19 and a standard deviation 5.

Find the mean, variance, and standard deviation for the following linear combinations of $\displaystyle {X}$ and $\displaystyle {Y}$ .

$\displaystyle {5}{X}+{Y}$
Mean:
Variance:
Standard Deviation:

$\displaystyle {X}-{3}{Y}$
Mean:
Variance:
Standard Deviation:

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