Question

John and Jane are working on a project, and all of their project meetings are scheduled to start at 9:05. John always arrives promptly at 9:05. Jane is highly disorganized and arrives at a time that is uniformly distributed between 8:33 and 10:31. The time (measured in minutes, a real number that can take fractional values) between 8:33 and the time Jane arrives is thus a continuous, uniformly distributed random variable.

What is the expected duration of time (measured in minutes, a real number that can take fractional values) John waits for Jane to arrive?

Round your answer to three decimal digits after the decimal point.

Answer 1

Let T be the time John waits for Jane to arrive and X be the time in minutes after 8:33 on which Jane arrives.

X ~ Uniform(0, 118) (Time difference between 8:33 and 10:31 is 118 minutes)

The distribution of T is given as,

T = 0 for X 32   (Time difference between 8:33 and 9:05 is 32 minutes)

T = X - 32 for 32 < X < 118

Expected duration of time = E(T) =

= 31.339 minutes