**Exercise 7.** UCLA researchers monitor the number of residential burglaries occurring in a particular 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 \( P(X \geq 6) \). 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 \( P(X \geq 6) \) by a finite sum like \( P(6 \leq X \leq 10) \).(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.

"Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you. To get remaining sub-parts solved, please repost the complete question and mention the sub-parts to be solved." As Prof. P. K. Giri said "A discrete random variable is a variable whose values can be obtained by counting. Though, the values can range infinitely, therefore, a discrete random variable is countably infinite." The number of students in a class, the number of road accidents in a particular city - these are the example of discrete random variable.Here, i) the number of burglaries can range between 0 and infinity ii) the number of burglaries must be an integer Under these conditions we can say that, with Answer: The appropriate model for X is P(λ=3).We have, Answer: The value of P(X = 0) is 0.0498.We have, Answer: The value of P(X≥6) is 0.0839.