Discrete probability distribution

It is also expedient to verify that the selected distribution eectively models the data because anything short of almost accurate could prove detrimental to future predictions. Hogg and Klugman (1984) serves as a standard reference for this subject. Adeleke and Ibiwoye (2011) used these same concepts to…

announced by the state. The winner gets a prize. The probability that the correct 3 digits in the right order is selected is at an odds of 1 in 1,000. So if If a ticket costs two dollars and the winner must pick a sequence of five digits then if There are 10^5=100,000 different combinations of 5 digit numbers and only the right combination wins the probability to win is at a 1 in 100000 chance to win. The chance to lose the 2 dollars put in is at a probability of 99999 in 100000 chance. Even if…

results that are almost certain. The Law of Large Numbers is “A law expressing the fact that if a trial in which all outcomes are independent of each other and equally likely is repeated, then the relative frequency of each outcome approximates its probability with increasing accuracy as the number of repetitions becomes sufficiently large” is the definition given for law of large numbers (Law of Large Numbers). The application of weak law of large…

In the book “the Signal and the noise”, author Nate Silver talks about prediction from many different angles. Silver explains how prediction is a part of our everyday life and how it affects us. From math to history, inside of a class room or on a court/field, prediction is something we deal with on a day to day basis unconsciously. Silver talks about the benefits of failure and how failure is helpful in the long run with making predictions. Throughout the years we have made progress with…

The Randomness of the Universe In the movie, Match Point, directed by Woody Allen, the scales of fate and justice in society are determined by the mere uncertainties of the universe, in other words, by random chance. Chance is the random occurrences that people experience every day, and is a result of entropy. Based on the second law of thermodynamics, the universe has a tendency to move towards disorder or a randomness. This characteristic of entropy can explain how fate is actually an…

the prior distribution, which quantifies the belief about the parameters before measurements. The prior distribution and likelihood function can be multiplied together to form a proportion to the posterior distribution which represents knowledge about the unknown parameters after the data has been observed [3]. We begin with an introduction to the basic steps in Bayesian analysis followed by defining the important terminologies in Bayesian methods which are “prior and posterior distributions”…

s: Translations are the process of moving around all of the coordinates that make up a shape. All the points move the same distance in the same direction. The transformation is isometric which means that it does not change in shape or sides. If the pre-image moves either right or up the coordination would be adding. If the pre-image moves either left or down the image would be subtraction. The picture to the right is an example of translation. The answer to the question at the bottom would be…

The general model introduced in Fig.4.10 is commonly used to design stable high-order modulators. If a chain of integrators is used to form the loop filter, two main modulators typologies exist [1, 5, 8]: a cascade of M delaying integrators is used to form the filter, where the feedback and the input signals are being fed to each integrator input with different weight factors a_i and b_i (Fig.4.11). The transfer function of the signal filter, L_0, is: while the feedback filter L_1 can be…

exact probability model for the number of automobile accidents over the past year for the 50 medical interns? (Note: The 11 reported accidents include both police-reported and non-police-reported accidents). Answer:- Fixed Proportion = .065 Number of interns involved in accident last year = total number of interns*.065. n = .065*It where n denoted interns in an accident and It denotes the total number of interns. P(n) = ItCn*.065^n*.935^(It-n)......from .binomial probability distribution the…

One of the many questions posed by those searching for answers on Just Noticeable Difference was if JND could be a suitable as a unit of measure. Analyzing data from two prior experiments, where participants were to discriminate different colors when shown different brightness intervals and applying it to sound also. Once all the data was analyzed, the researchers determined that JND could not be used as a unit of measure (Newman, 1933). Although JND could not be used as a unit of measurement,…