Probability_Distributions

Probability Distributions Report '''''''''''' '''''''''' Applied Business Research and Statistics QNT 531 ''''''''''''''' August 2, 2010 Abstract Statistical functions that describe all the possible values and likelihoods that a random variable can take within a given range are referred to as probability distribution. While examining probability distribution I found there are two forms, cumulative, and uniform distribution. I used the example of flipping a coin to exhibit the cumulative probability if the coin flips would result in one or fewer heads. To show the uniform distribution I used tossing a die to demonstrate the probability that the die will land on the number six. Probability distribution can be discrete or continuous, the example I used for discrete was, if I tossed a coin six times, and the coin landed two heads or three heads but not two and one half. To demonstrate continuous probability, I examined a company’s investors or executives determining the possible returns that a stock may yield in the future. Basically this report is expressing on a day-to-day basis probability distribution is incorporated most decisions we make. Probability distributions report Probability distribution is defined as, “A statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. This range will be between the minimum and maximum statistically possible values, but where the possible value is likely to be plotted on the probability distribution depends on a number of factors, including the distributions mean, standard deviation, skewness and kurtosis.” ("Statistics Tutorial: Probability Distributions", 2010, p. 2) Probability distribution comes in two flavors cumulative and uniform distribution. A cumulative probability “refers to the probability that the value of a random variable falls within a specified range” ("Statistics Tutorial: Probability Distributions", 2010, para. 5). A good example would be flipping a coin. If I flipped the coin two times, what is the probability that the coin flips would result in one or fewer heads' The answer would exhibit a cumulative probability. It would be the probability that the coin flip experiment results in zero heads plus the probability that the experiment results in one head. More than likely a cumulative probability distribution would be signified within a table or an equation. The simplest probability distribution occurs when all of the values of a random variable occur with equal probability. This probability distribution is called the uniform distribution. The simplest example I can think of is a tossing a die. What is the probability that the die will land on the number six. When a die is tossed, there are six possible outcomes, each possible outcome is a random variable (X), and each outcome is equally likely to occur. So we have a uniform distribution. Consequently, the probability of the die landing on six is one-sixth or expressed P(X = 6) = 1/6 ("Probability Distribution", 2009, p. 1). The university reading described two functions of probability distribution as discrete and continuous a discrete probability function is a function that can take a distinct number of values. This is most often the non-negative figures or some division of the non-negative integers. My research did not reveal any mathematical limitation suggesting discrete probabilities are always integers; the best way to explain is by using an example. If I tossed a coin six times, I could flip heads twice or three times but not flip two and one-half heads. The discrete value of the coin has a certain probability of occurrence between zero and one. The discrete function that allows negative values or values greater than one is not a probability function in the coin toss scenario. In other words if I were to plot points over a continuous interval, the probability at a single point is always zero or a continuous probability function. Probabilities are measured over intervals, not single points. I can find the probability for that interval by plotting the skew or the area under the curve between two distinct points defines. This means that the height of the probability function can be greater than one. The property that the integral must equal one is equivalent to the property for discrete distributions that the sum of all the probabilities must equal one. For instance, when a company’s investors or executives decide to determine the possible returns that the stock may yield in the future; they are in principle determining the stock's probability of distribution. This is accomplished by looking at the stock's history of returns, which can be measured on a time interval. I am not an analysis but from what I understand the time interval of a stock will likely be composed of only a fraction of the stock's returns, which will subject the analysis to sampling error. If the company investor or executive increase the sample size, this error will be dramatically reduced (Cooper & Schindler, 2006). In conclusion, probability distribution is incorporated in decisions we make on a day-to-day basis. The outcome depends on how effectively a person can identify the dependent and independent variables when it is presented. Walt Disney once stated, “We keep moving forward, opening new doors, and doing new things, because we’re curious and curiosity keeps leading us down new paths” (Walt Disney, 1935, para. 1). This principle of probability distribution could be applied in situations in which upper management needs to make an effective management decision. Knowing how to identify the problem and isolating the variables, which can affect the possible outcomes would help in areas of budget forecasting, product control, employee evaluations, and customer satisfaction. References Cooper, D. R., & Schindler, P. S. (2006). Business Research Methods (9th ed.). [Adobe Digital Editions]. Retrieved from https://ecampus.phoenix.edu Lind, D. A., Marchal, W. G., & Wathen, S. A. (2008). Statistical Techniques in Business & Economics (13th ed.). [Adobe Digital Editions]. Retrieved from https://ecampus.phoenix.edu Probability Distribution. (2009). Retrieved from http://www.teachmefinance.com/probabilitydistribution.html Statistics Tutorial: Probability Distributions. (2010). Retrieved from http://stattrek.com Walt Disney. (1935). Keep Moving Forward. Retrieved from http://www.cartoonbrew.com/disney/keep-moving-forward.html