Let X be a numeric random variable with E[X] = 4 and V [X] = 5.
Let Z be a linear transformation with Z = 5X + 10. Compute E[Z]
and V [Z].
2. Suppose you want to order a pizza from your favorite pizzeria. You
know from your past experience that, after ordering, Y: ” The waiting
time until the pizza is delivered [in minutes]" is normally distributed
with Y ? N (15, 4).
(a) What is the probability that you will wait less than 10 minutes,
i.e. P (Y ? 10)?
(b) What is the minimum amount of time that you will wait with a
probability of 95% (i.e. P (Y ? y) = 0.95)?
(Note: You may use a statistical software to compute the answers.) 2
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