Homework 4 A toll booth costs 1 dollar for cars and 2 dollars for trucks. Suppos
ID: 3330380 • Letter: H
Question
Homework 4 A toll booth costs 1 dollar for cars and 2 dollars for trucks. Suppose that 30% of the vehicles passing through the booth are trucks. Suppose we observe the next 50 vehicles and observe whether they are cars or trucks, and that each vehicle is independent. Let Y = the number of trucks in the next 50 vehicles 1 a. What is the distribution of ? (Give the family and parameters) b. What is the probability that exactly 20 of the next 50 vehicles are trucks? c. What are the mean and variance of Y d. Let R = the amount of revenue for the next 50 vehicles, write a formula for R in terms of Y. Calculate E[R) and VIR) using the linear transformation shortcut e.Explanation / Answer
Ans:
a)Y will follow Binomial distribution with n=50,p=0.3
b)P(y=20)=BINOMDIST(20,50,0.3,FALSE)=0.0370
c)mean=E[Y]=np=50*0.3=15
variance=Var(Y)=np(1-p)=50*0.3*0.7=10.5
d)R=2y+1*(50-y)=y+50
e)E[R]=E[Y]+50=15+50=65
Var(R)=10.5
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