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Lectures for STP 421: Probability Theory
Lectures for STP 421: Probability Theory

Point estimation
Point estimation

... If we take several sample and find mean of the sample, therefore the distribution of the sample mean called sampling distribution of the sample mean, X . For example, suppose you sample 50 students from your college regarding their mean GPA. If you obtained many different samples of 50, you will com ...
Curriculum Guide (Word)
Curriculum Guide (Word)

... (9#1) domain – set of values of the independent variable of a function range – possible values for y in a function function – relation when the value of x has a value of y ...
practice exercises for exam 2
practice exercises for exam 2

2016-17 7th Grade Math Guide
2016-17 7th Grade Math Guide

... a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Fo ...
History and Social Science Standards of Learning for Virginia
History and Social Science Standards of Learning for Virginia

... AFDA.6 The student will calculate probabilities. Key concepts include a) conditional probability; b) dependent and independent events; c) addition and multiplication rules; d) counting techniques (permutations and combinations); and e) Law of Large Numbers. AFDA.7 The student will analyze the normal ...


... because if the die were tossed repeatedly (as in some games or gambling situations) then each number would occur close to 1/6 of the time. However, if the die were weighted in some way, these numerical values would not be so useful. Note that if we wish to consider some compound event, the probabili ...
Li Jie
Li Jie

... and another random variable YN(0,1), COV(X,Y)= -1, find variance and covariance of V=4X+3Y+1 and W=-2X+4Y Var (V )  Var (4 X  3Y  1)  16Var ( X )  9Var (Y )  24Cov( X , Y ) Var (W )  Var (2 X  4Y )  4Var ( X )  16Var (Y )  16Cov( X , Y ) ...
3. Covariance and Correlation
3. Covariance and Correlation

... The concept of best linear predictor is more powerful than might first appear, because it can be applied to transformations of the variables. Specifically, suppose that X and Y are random variables for our experiment, taking values in general spaces S and T , respectively. Suppose also that g and h ...
Lecture 20 - Mathematics
Lecture 20 - Mathematics

What is a P-value? I have found that many students are unsure
What is a P-value? I have found that many students are unsure

Chapter 1: Exploring Data
Chapter 1: Exploring Data

The Practice of Statistics
The Practice of Statistics

TPS 4e Chapters 1-7 Guided Reading Notes Word File
TPS 4e Chapters 1-7 Guided Reading Notes Word File

Springer Series in Statistics
Springer Series in Statistics

Ballot theorems, old and new
Ballot theorems, old and new

Chapter 5: Interval estimation and testing
Chapter 5: Interval estimation and testing

(ab)use of statistics in the legal case against the nurse
(ab)use of statistics in the legal case against the nurse

... to kill some of her patients. The word ‘ward’ is not mentioned in these questions nor is there any mention of the other nurses who worked there. It was the choice of Elffers himself to consider the level of wards. We do not claim that this decision was wrong; there are arguments to defend it, the mo ...
the effect of body size on cottonmouth (agkistrodon piscivorus)
the effect of body size on cottonmouth (agkistrodon piscivorus)

... parameterizations of temporal variation in survival or recapture probability the ‘year’ and ‘season’ explanatory variables, respectively. To determine whether our data met the assumptions of the CJS estimator, we first developed a ‘global’ model containing all main effects (year, season, sex, and a ...
Chapter 5 Slides
Chapter 5 Slides

4 Continuous Random Variables and Probability Distributions
4 Continuous Random Variables and Probability Distributions

On the inelastic collapse of a ball bouncing on a randomly
On the inelastic collapse of a ball bouncing on a randomly

X - IE230
X - IE230

... • The Erlang distribution is a generalization of the exponential distribution. • The exponential distribution models the interval to the 1st event, while the Erlang distribution models the interval to the rth event, i.e., a sum of exponentials. • If r is not required to be an integer, then the distr ...
Chapter 4 (Continuous RVs)
Chapter 4 (Continuous RVs)

... • The Erlang distribution is a generalization of the exponential distribution. • The exponential distribution models the interval to the 1st event, while the Erlang distribution models the interval to the rth event, i.e., a sum of exponentials. • If r is not required to be an integer, then the distr ...
Boosting the Margin
Boosting the Margin

... (x,y) is chosen according to D (the distribution from which examples are generated). This is abbreviated PD[A] We use P(x,y)-S[A] to denote the probability with respect to choosing an example uniformly at random from the training set. This is abbreviated PS[A] ...
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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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