I am given E[3Z + 10] = 4, and Var[3Z + 10] = 36. How would I go about solving for the mean and variance of Z? I assume its not as simple as subtracting and dividing to solve for Z with either case...I also realize "3Z + 10" is included with both sides, which might be a give away to simplify but I am still unsure. Thank you.
2026-03-26 21:07:15.1774559235
Deriving expected value and variance from given expected value and variance
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Use: $E(3Z+10)=3EZ+10$ and $var(3Z+10)=var (3Z)=3^{2}var(Z)$.