Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. The term "mathematical statistics" is closely related to the term "statistical theory" but also embraces modelling for actuarial science and non-statistical probability theory, particularly in Scandinavia.
Description: it trains the intuition to acquire probabilistic feeling. This book explains every single concept it enunciates. This is its main strength, deep explanation, and not just examples that happen to explain Tsitsiklis and Bertsekas leave nothing to chance. The probability to misinterpret a concept or not understand it is just... zero. Numerous examples, figures, and end-of-chapter problems strengthen the understanding. Also of invaluable help is the book's web s...
Introduction to the law of large numbers
Random variables. Expected value. Probability distributions (both discrete and continuous). Binomial distribution. Poisson processes.
Manually going through the combinatorics to determine the probability of an event occuring
Basics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int
A different way to think about the probability of getting 2 heads in 4 flips
Venn diagrams and the addition rule for probability
Basics of probability and combinatorics. What is the probability of getting a diamond or an ace from a deck of cards? Well I could get a diamond that is not an ace, an ace that is not a diamond, or the ace of diamonds. This tutorial helps us think these t
Probability of exactly 3 heads in 5 flips using combinations
Basic idea and definitions of random variables
Defining discrete and continuous random variables. Working through examples of both discrete and continuous random variables.
Expected value of a random variable
Conceptual understanding of where the formula for binomial coefficients come from
Thinking about the different ways we can pick officers in order to find the probability of one situation in particular.
Example of figuring out the probability of picking a non-blue marble from a bag.
Basics of probability and combinatorics.
Probability of compound events. The Addition Rule. Common Core Standard 457 S-CP. 7
Deciding whether you want to play a game at a strange casino.
Basics of probability and combinatorics. What's the probability of picking two e from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you
Thinking about how the probability of an event can be dependent on another event occuring.
The probability of picking a yellow marble from a bag.
Working out the probability of pulling a yellow marble from a bag of multi-colored marbles.
Pearson's Chi Square Test (Goodness of Fit)
Making inferences based on sample data. Confidence intervals. Margin of error. Hypothesis testing.
Chi-Square Distribution Introduction
Contingency Table Chi-Square Test