A Stat 510 student works at the IT Help Desk at Hale Library. She works there Tuesdays
and Thursdays 6 pm - 10 pm and on Sunday 1 pm - 5 pm. On average, she receives 2.4
walk-ins per shift on Tuesdays and Thursdays and 3.2 walk-ins on Sundays.
Assume walk-in arrivals occur randomly at a constant rate, and different periods of time
are independent.
Assume that the proportion of walk-in problems that have a quick solution follows a Beta
distribution.
5. Let r.v. $X$ = the time in hours until her first walk-in on a Tuesday shift. What is the
distribution of $X$?
Hint: How many hours are in a shift?
a. $X \sim \text{Exp}(0.6)$
b. $X \sim \text{Exp}(2.4)$
c. $X \sim \text{Gamma}(4, 2.4)$
d. $X \sim \text{Gamma}(1, 2.4)$
e. $X \sim \text{Gamma}(4, 0.6)$
f. $X \sim \text{Gamma}(1, 0.6)$
g. None of the above.
6. FORMULA. What is the probability that she will wait more than 1.5 hours for the
first customer of a Sunday shift? (Use four digits after the decimal point, e.g., 0.1234)