Question

Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time. (a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv's X1, X10 and use a rule of expected value.] min (b) What is the variance of your total waiting time? (Round your answer to two decimal places.) min 2 evening time. Round the variance to two decimal places.) (c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time expected value min variance min2 (d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time – evening time. Assume a week includes only Monday through Friday.) expected value min variance min 2

Answer 1

since for uniform distribution: U(a,b)

mean =(a+b)/2 and Variance =(b-a)²/12

a) total expected waiting time for a week =5*((0+8)/2+(0+10)/2) =45

b)

Variance =5*((8-0)^2/12+(10-0)^2/12)=68.33

c)

expected value=(0+8)/2-(0+10)/2 =-1

Variance =((8-0)^2/12+(10-0)^2/12)=13.67

d)

expected value = -5

Variance =68.33