Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.

A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.223, 0.335, 0.251, 0.126, and 0.047, respectively.

Thank you for the opportunity to help you with your question!

Hi, Elsa! So this is NOT a probability distribution. The reason why it is not a probability distribution is because all values reported in a given day must equal 1. .223+.335+.251+..126+.047 = .982. So, this is is less than 1 and does not equal 1.

In order to satisfy requirement for probability distribution, we need to add a car theft that would equal to 1. Since we don't know what the exact probability of 5 car thefts are, we must add X>4= probability of .018 . Adding the probability of .018 brings the probability up to 1 which would satisfy the requirement.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Jun 16th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.