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Exercise 7. UCLA researchers monitor the number of residential burglaries occurring in a partic- ular Los Angeles neighborhood. They find, on average that 3 burglaries occur in the neighborhood in each year. Let X be the number of burglaries that occur in one year. (a) What is an appropriate model for X? Briefly justify your answer, and how you choose any parameters in your model. (b) Find P(X = 0). (c) Calculate the probability that P(X ≥ 6). Formally, this involves summing a series with infinitely many terms. You will need to calculate some terms and show that they decrease fast enough that you can approximate P(X ≥ 6) by a finite sum like P(6 ≤ x ≤ 10).

Exercise 7. UCLA researchers monitor the number of residential burglaries occurring in a partic- ular Los Angeles neighborhood. They find, on average that 3 burglaries occur in the neighborhood in each year. Let X be the number of burglaries that occur in one year. (a) What is an appropriate model for X? Briefly justify your answer, and how you choose any parameters in your model. (b) Find P(X = 0). (c) Calculate the probability that P(X ≥ 6). Formally, this involves summing a series with infinitely many terms. You will need to calculate some terms and show that they decrease fast enough that you can approximate P(X ≥ 6) by a finite sum like P(6 ≤ x ≤ 10).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Exercise 7. UCLA researchers monitor the number of residential burglaries occurring in a partic- ular Los Angeles neighborhood. They find, on average that 3 burglaries occur in the neighborhood in each year. Let X be the number of burglaries that occur in one year. (a) What is an appropriate model for X? Briefly justify your answer, and how you parameters in your model. (b) Find P(X = 0). (c) Calculate the probability that P(X ≥ 6). Formally, this involves summing a series with infinitely many terms. You will need to calculate some terms and show that they decrease fast enough that you can approximate P(X ≥ 6) by a finite sum like P(6 ≤ X ≤ 10). (d) One year, there are 6 or more burglaries in the neighborhood; i.e. twice the usual number. Residents argue that the crime rate has gone up. Using your answer from (c), explain why the crime rate has not necessarily gone up in that year. choose any
Transcribed Image Text:Exercise 7. UCLA researchers monitor the number of residential burglaries occurring in a partic- ular Los Angeles neighborhood. They find, on average that 3 burglaries occur in the neighborhood in each year. Let X be the number of burglaries that occur in one year. (a) What is an appropriate model for X? Briefly justify your answer, and how you parameters in your model. (b) Find P(X = 0). (c) Calculate the probability that P(X ≥ 6). Formally, this involves summing a series with infinitely many terms. You will need to calculate some terms and show that they decrease fast enough that you can approximate P(X ≥ 6) by a finite sum like P(6 ≤ X ≤ 10). (d) One year, there are 6 or more burglaries in the neighborhood; i.e. twice the usual number. Residents argue that the crime rate has gone up. Using your answer from (c), explain why the crime rate has not necessarily gone up in that year. choose any
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