Question: The length of time a coworker takes for lunch can be modeled by the following continuous distribution:

\(f\left( x \right)=\frac{1}{30}{{e}^{-\frac{x}{30}}},\,\,\,x\ge 0\)

where x is measured in minutes.

(a) What is the probability that lunch takes less than 60 minutes?

(b) What is the expected length of lunch?

(c) What is the variance of the length of lunch?

(d) Let Y = 2X + 5

i. What is the expected value of Y?

ii. What is the variance of Y?