Continuous Probability Distributions & Probabilty Densities Week 6
The true logic of this world is the calculus of probabilities. - James Maxwell Continuous Random Variables When random variables are continuous they generate probability density functions. Uniform Random Variable The Normal Random Variable The most widely used probability model in statistics is the Gaussian or normal distribution. The normal distribution is a pdf whose graph is bell-shaped, symmetrical, and single peaked. The mean, median and mode coincide and lie at the center of the distribution located at x = 0. The two tails extend indefinitely and are asymptotic to the x-axis. A normal distribution is fully specified by two parameters - mean and the standard deviation.
The Exponential Random Variable queueing theoryIn computer science, queueing theory is the study of queues as a technique for managing processes and objects in a computer. A queue can be studied in terms of: the source of each queued item, how frequently items arrive on the queue, how long they can or should wait, whether some items should jump ahead in the queue, how multiple queues might be formed and managed, and the rules by which items are enqueued and dequeued. The queues that a computer manages are sometimes viewed as being in stacks. In most systems, an item is always added to the top of a stack. A process that handles queued items from the bottom of the stack first is known as a first-in first-out (FIFO) process. A process that handles the item at the top of the stack first is known as a last-in first-out (LIFO) process. -- from Whatis.com The Gamma, Exponential and Chi-Square Distributions The Student t The Beta Distribution Fitting a Distribution to Data
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