Q3: Suppose that your morning waiting time for a bus has a uniform distribution on the interval

from 0 to 5 min, and your afternoon waiting time also has this distribution. Then if x denotes the

total waiting time on any particular day, the density function of x can be shown to be

.04x

for 0

for 5

f(x)=4-.04x

0

for other values of x

a. Draw the density curve, and verify that f(x) specifies a legitimate distribution.

b. In the long run, what proportion of your total daily waiting times will be at most 3 min? At least

7 min? At least 4 min? Between 4 min and 7 min?

c. What value separates the longest 10% of your daily waiting times from the remaining 90%?