Public policy and political science camden, New jersey, has one of the highest c

Question

Public policy and political science camden, New jersey, has one of the highest crime rates in the United States. As a result, a new camden county Police Department will include 400 officers and be responsible for an area convering nine square miles. ^5 Suppose the number of times a police cruiser from this new deaprtment drives through the whitman park neighborhood during a one-hour period is a ranfom vaiable X, with probability distribution as given in the table below Suppose a one-hour period is randomly selected a. What is the probability that no police cruiser will drive through the neighborhood? b.What is the probability that at least one police cruiser with drive through the beighborhood? C. What is the probability that at most two police cruisers will drive through the neighborhood? D. what is the probability that more than seven police cruisers will drive through the neighborhood? e. Suppose at lease tow police crusiers were sighted in the neighborhood during the one-hour period. What is the probability that there were at least four during this time?

Explanation / Answer

Sum of total probabilities=P(x<=7)=0.3679+0.3679+0.1839+0.0613+0.0153+0.0031+0.0005+0.0001=1

a)P(x=0)=0.3679

b)P(x>=1)=1-P(x<1)=1-P(x=0)=1-0.3679=0.6321

c)P(x<=2)=P(x=0)+P(x=1)+P(x=2)=0.3679+0.3679+0.1839=0.9197

d)P(x>7)=1-P(x<=7)=1-1=0

e)P(x>=4|x>=2)=P(x>=4)/P(x>=2)

=(0.0153+0.0031+0.0005+0.0001)/(0.1839+0.0613+0.0153+0.0031+0.0005+0.0001)

gives P(x>=4|x>=2)=0.0719

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