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lena : probability   58

Probability, Statistics and Random Processes | Free Textbook | Course
This probability and statistics textbook covers:

Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods
Single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities
Limit theorems and convergence
Introduction to mathematical statistics, in particular, Bayesian and classical statistics
Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion
Simulation using MATLAB and R
books  probability  statistics  math 
12 days ago by lena
A Bayesian view of Amazon Resellers | beta-binomial model
After observing 2 positive reviews, our posterior estimate on θB has a beta(3, 1) distribution. The probability that a sample from θA is bigger than a sample from θB is 0.713. That is, there’s a good chance you’d get better service from the reseller with the lower average approval rating.
bayes  probability  statistics 
6 weeks ago by lena
The Coin Flip: A Fundamentally Unfair Proposition?
If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. (If it starts out as heads, there's a 51% chance it will end as heads).
If the coin is spun, rather than tossed, it can have a much-larger-than-50% chance of ending with the heavier side down. Spun coins can exhibit "huge bias" (some spun coins will fall tails-up 80% of the time).
If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.
If the coin is tossed and allowed to clatter to the floor where it spins, as will sometimes happen, the above spinning bias probably comes into play.
A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.
The same initial coin-flipping conditions produce the same coin flip result. That is, there's a certain amount of determinism to the coin flip.
A more robust coin toss (more revolutions) decreases the bias.
7 weeks ago by lena
Seeing Theory
A visual introduction to probability and statistics.
probability  statistics  visualization 
7 weeks ago by lena
Random: Probability, Mathematical Statistics, Stochastic Processes
Random is a website devoted to probability, mathematical statistics, and stochastic processes, and is intended for teachers and students of these subjects. The site consists of an integrated set of components that includes expository text, interactive web apps, data sets, biographical sketches, and an object library.
probability  statistics  visualization 
7 weeks ago by lena
Probability Primer - YouTube
A series of videos giving an introduction to some of the basic definitions, notation, and concepts one would encounter in a 1st year graduate probability course.

Videos less than 15 minutes each.
probability  math  statistics  video  elearning  towatch 
september 2018 by lena
Explained Visually
Explained Visually (EV) is an experiment in making hard ideas intuitive inspired the work of Bret Victor's Explorable Explanations.

Regression, PCA, Eigenvalues, Pi, Sine/Cosine, Markov chains, Probability
math  programming  statistics  probability  visualization  pca  matrix  markov 
august 2018 by lena
If correlation doesn’t imply causation, then what does? | DDI
I often wonder how many people with real decision-making power – politicians, judges, and so on – are making decisions based on statistical studies, and yet they don’t understand even basic things like Simpson’s paradox.
causality  statistics  probability  research  science 
july 2018 by lena
Probability questions : math
Hi all. Recently I devised a game, and was wondering about the math behind it. The game’s simple: - There’s a button and N lights. - Each light can be either ON or OFF - Whenever you press the button, a light is chosen and random, and has its state toggled (if it’s on it’s turned off, if it’s off it’s turned on). - You win the game when all the lights are ON - You cannot lose

My questions are:

If we have x lights on, what is the expected number of presses needed to win?

If we have x lights on...
probability  markov  math 
march 2018 by lena
David J. Aldous reviews
Reviews of popular science probability/statistics books
books  review  statistics  probability 
march 2018 by lena Probability Tales (Student Mathematical Library) (9780821852613): Charles M. Grinstead, William P. Peterson, J. Laurie Snell: Books
If you take a college course in Probability and find it less relevant to interesting aspects of the real world than you had hoped, then I strongly recommend this book as the way to rekindle your interest. It has three long chapters (on streaks in sports and elsewhere; the stock market; lotteries) and a shorter chapter on fingerprints. All are interesting and well written, and the first two in particular examine in substantial detail how the math and the data are related. Are streaks longer than ...
probability  books  statistics  wishlist 
march 2018 by lena
The Probability and Statistics Cookbook
The probability and statistics cookbook is a succinct representation of various topics in probability theory and statistics. It provides a comprehensive mathematical reference reduced to its essence, rather than aiming for elaborate explanations.
probability  statistics  reference  math 
january 2018 by lena
stochastic processes - Intuitive explanation for periodicity in Markov chains - Cross Validated
A state i has period k if any return to state i must occur in multiples of k time steps. Formally, the period of a state is defined as

k = gcd{n:Pr(Xn=i|X0=i)>0}gcd{n:Pr(Xn=i|X0=i)>0}
(where "gcd" is the greatest common divisor). Note that even though a state has period k, it may not be possible to reach the state in k steps. For example, suppose it is possible to return to the state in {6, 8, 10, 12, ...} time steps; k would be 2, even though 2 does not appear in this list.
probability  math  markov 
november 2017 by lena
Chebyshev's inequality - Wikipedia
In probability theory, Chebyshev's inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution's values can be more than k standard deviations away from the mean
probability  statistics 
november 2017 by lena
Ross–Littlewood paradox - Wikipedia
The problem starts with an empty vase and an infinite supply of balls. An infinite number of steps are then performed, such that at each step 10 balls are added to the vase and 1 ball removed from it. The question is then posed: How many balls are in the vase when the task is finished?
The problem is ill-posed. To be precise, according to the problem statement, an infinite number of operations will be performed before noon, and then asks about the state of affairs at noon. But, as in Zeno's paradoxes, if infinitely many operations have to take place (sequentially) before noon, then noon is a point in time that can never be reached. On the other hand, to ask how many balls will be left at noon is to assume that noon will be reached. Hence there is a contradiction implicit in the very statement of the problem, and this contradiction is the assumption that one can somehow 'complete' an infinite number of steps. This is the solution favored by mathematician and philosopher Jean Paul Van Bendegem.
september 2017 by lena
Nicole White
Find the Steady State Distribution of a Markov Process in R.
r  math  probability 
september 2017 by lena
Q–Q plot - Wikipedia
A normal Q–Q plot of randomly generated, independent standard exponential data, (X ~ Exp(1)). This Q–Q plot compares a sample of data on the vertical axis to a statistical population on the horizontal axis. The points follow a strongly nonlinear pattern, suggesting that the data are not distributed as a standard normal (X ~ N(0,1)). The offset between the line and the points suggests that the mean of the data is not 0. The median of the points can be determined to be near 0.7

A normal Q–Q plot comparing randomly generated, independent standard normal data on the vertical axis to a standard normal population on the horizontal axis. The linearity of the points suggests that the data are normally distributed.

A Q–Q plot of a sample of data versus a Weibull distribution. The deciles of the distributions are shown in red. Three outliers are evident at the high end of the range. Otherwise, the data fit the Weibull(1,2) model well.

A Q–Q plot comparing the distributions of standardized daily maximum temperatures at 25 stations in the US state of Ohio in March and in July. The curved pattern suggests that the central quantiles are more closely spaced in July than in March, and that the July distribution is skewed to the left compared to the March distribution. The data cover the period 1893–2001.
In statistics, a Q–Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.[1]
probability  statistics 
september 2017 by lena
Canadian calculus - tasty math | Ask MetaFilter
So Bud Light is selling cases of 28 bottles (yes, 28) with NHL team logos on the caps

1. There are 30 teams in the NHL. I bought 3 cases and have 27 of the 30 teams. Am I lucky, unlucky or right on probability-wise?

2. How many more cases SHOULD get me to 30/30.
september 2017 by lena
Statlect, the digital textbook
Free online textbook on math, statistics and probability
books  free  math  statistics  probability 
august 2017 by lena
When intuition and math probably look wrong (boy born on Tuesday problem) | Science News
Everything depends, he points out, on why I decided to tell you about the Tuesday-birthday-boy. If I specifically selected him because he was a boy born on Tuesday (and if I would have kept quiet had neither of my children qualified), then the 13/27 probability is correct. But if I randomly chose one of my two children to describe and then reported the child’s sex and birthday, and he just happened to be a boy born on Tuesday, then intuition prevails: The probability that the other child will be a boy will indeed be 1/2. The child’s sex and birthday are just information offered after the selection is made, which doesn’t affect the probability in the slightest.
probability  math  statistics 
july 2017 by lena
When Intuition And Math Probably Look Wrong - Science News
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
math  probability 
june 2010 by lena
Warning Signs in Experimental Design and Interpretation
statistics  science  research  probability  media 
may 2009 by lena
Jeff Atwood’s exercise in Bayesian probability « The Pageman in Kabul
Another post on the Boy/Girl problem with a nice picture explanation and links to other posts about the topic
probability  statistics 
january 2009 by lena

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