Worksheet 11: Random numbers
... Task 11.1: Quality analysis of random number sequences (6 points) The data needed in this worksheet can be found in the file ws11.pkl.gz on the home page. The data file contains five data sets of 100000 apparently random numbers in the interval [0, 1]. Actually only one of those sequences was genera ...
... Task 11.1: Quality analysis of random number sequences (6 points) The data needed in this worksheet can be found in the file ws11.pkl.gz on the home page. The data file contains five data sets of 100000 apparently random numbers in the interval [0, 1]. Actually only one of those sequences was genera ...
Spreadsheet Modeling & Decision Analysis:
... The Uncertainty of Sampling The replications of our model represent a sample from the (infinite) population of all possible replications. Suppose we repeated the simulation and obtained a new sample of the same size. Q: Would the statistical results be the same? A: No! As the sample size (# o ...
... The Uncertainty of Sampling The replications of our model represent a sample from the (infinite) population of all possible replications. Suppose we repeated the simulation and obtained a new sample of the same size. Q: Would the statistical results be the same? A: No! As the sample size (# o ...
Prep for Exam 1 Thursday 8-14-06 (36 Kb ) STT 315 Fall 2006
... even if all outcomes are not equally probable. Loosely put: It is because such rules are preserved when we derive any probability model from another one using the rules and also the rules must apply if our probabilities are to conform to real world counts (since counts are the basis for classical pr ...
... even if all outcomes are not equally probable. Loosely put: It is because such rules are preserved when we derive any probability model from another one using the rules and also the rules must apply if our probabilities are to conform to real world counts (since counts are the basis for classical pr ...
Binomial Distribution
... Note that if the sample size, n, is less than 5% of the population, the independence assumption is not of great concern. Therefore the acceptable sample size for using the binomial distribution with samples taken without replacement is [n<5% N] where n is equal to the sample size, and N stands for ...
... Note that if the sample size, n, is less than 5% of the population, the independence assumption is not of great concern. Therefore the acceptable sample size for using the binomial distribution with samples taken without replacement is [n<5% N] where n is equal to the sample size, and N stands for ...
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)