Decision_of_Uncertainty_Paper

Decision of Uncertainty Paper The use of statistical data in decision making can be very helpful. Being able to use the statistics and formulate probabilities to help in the decision making process. There are several different types of statistical processes such as using confidence intervals, calculation of probability (Bayes’ Theorem), and hypothesis testing. Decision       I am going out of town for vacation for a month and the decision has to be made on whether to purchase a home security system or take the chance of not having any defense. The reason for this is because leaving a house empty for a month is a risk. However, purchasing a home security system is a rather expensive investment. With the fact that I am on a strict budget I have not allocated funds for such an investment.       There are many people out there that like to rob houses. When robbers are “scoping” out their house or building they look at things such as the times people are there and the neighborhood. In this case if someone wanted to break in then it would be easy for them to see that no one is at home during this month. With a house sitter it will show activity at the house so therefore, it reduces the chances of the house getting broke into. Research       It has also been noted that robbers check things such as if anyone answers the landline or if the lights are on. Some may even find a reason to knock on the door just to see if anyone answers. It has been advised that when on vacation someone either stop by periodically or house sit for the one on vacation so the house does not look abandoned (Schroeder, 2010). It is said that 134 households out of 1000 will be burglarized, that would equate to 13 percent. The probability the homes which were burglarized did not have a home security system is 57 percent. The probability the homes which were burglarized did have a home security system installed is 14 percent(Fishman, 2003). Bayes’ Theorem  For the translation of the data and research that has been completed and collected the Bayes’ Theorem shall be used. Bayes’ Theorem is perfect for this decision because the evidence for this problem is very subjective. Bayes’ Theorem uses subjective probability where the opinions and information are interpreted as probabilities for calculation purposes. Thus, the confidence levels for the burglary of homes, burglary of homes with security systems, and burglary of homes without security systems will be predicted using Bayes’ Theorem.  Now that I have chosen the proper method to solve this problem I will input the numbers and calculate the confidence levels for all of the given subjective evidence. Not being burglarized will be notated by A1 and being burglarized will be notated by A2. I know that the probability of not being burglarized in general is 87%. So, the probability of being burglarized is 13%.   The notation and probability for not being burglarized with a home security system is P(B/A1) = .86. The notation and probability for being burglarized and having a home security system is P(B/A2) = .14. Using Bayes’ Theorem to find the confidence level that shows that I will not be burglarized if a home security system is installed the equation would look like the following: P(A1/B) = P(A1)*P(B/A1) divided by P(A1)*P(B/A1)+P(A2)*P(B/A2) P(A1/B) = (.87*.86)/((.87*.86)+(.13*.14)) P(A1/B) = .7482/.7664 P(A1/B) = .9763 = .98  After the above calculations it shows that the probability of my home being burglarized with a home security system is .02 and the probability of my home not being burglarized with a home security system is .98. Conclusion  The decision we make today will affect our lives for years to come. After deep research, observation of information, and the calculation of confidence levels using Bayes’ Theorem I can conclude that the better investment and wiser decision will be to install a home security system. The money allocated for my vacation can be used for the system at this time for the sake of my home and the valuable possessions in my home. Reference Fishman, Dr. Gideon; Hakim, Dr. Simon; Shachmurove, Dr. Yochanan. (2003). Do Burglars Calculate ROI' A Logistic Regression Analysis. Retrieved on July 4, 2010 from http://www.secondmoment.org/articles/burglars.php. Schroeder, S. (March 2010) How Robbers Did Their Dirty Deed Before Foursquare. Retrieved on July 4, 2010 from http://mashable.com/2010/02/19/how-robbers-did-their-dirty-deeds/.