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ELEMENTARY THEORETICAL PROBABILITIES

  • Statistics
On 10/03/2022

There are several approaches to determine the probability of an event. One of them is what we call the classical or theoretical probability. Mathematically, the theoretical probability is obtained by dividing the number of the elements of the set calledRead More

THE THEOREM OF TOTAL PROBABILITY AND BAYES’ RULE

  • Statistics
On 07/03/2022

Case Study In a certain assembly plant, three machines, M1, M2, and M3, make 20%, 30%, and 50%, respectively, of the products. It is known from past experience that 4%, 3%, and 5% of the products made by each machine,Read More

COVARIANCE AND CORRELATION MATRICES

  • Statistics
On 27/02/2022

Variance and correlation matrices play a vital role in multivariate statistics. Multivariate statistics studies n x p data from a set of samples, where n is the sample size or the number of measurements and p is the number ofRead More

THE SPECTRAL DECOMPOSITION OF SYMMETRIC MATRICES

  • Linear Algebra
On 24/02/2022

The picture above is an application of singular value decomposition in image processing. This post will discuss a special case of SVD, where the matrix to be decomposed is a symmetric matrix. The study of symmetric matrices is important inRead More

INDEPENDENT EVENTS

  • Statistics
On 23/02/2022

The above symbols represent the 52 cards of a deck of playing cards. If a card is selected at random from the deck then each of the 52 signs above is a member of the sample space. So the sample spaceRead More

THE BINOMIAL DISTRIBUTION

  • Statistics
On 23/02/2022

Suppose that a fair coin is tossed 20 times. (The word ‘fair’ here means that each side of the coin has the equal probability of appearing.) If it turned out that the coin came up heads 18 times (out ofRead More

SINGULAR VALUE DECOMPOSITION

  • Statistics
On 20/02/2022

In the article The Spectral Decomposition of Symmetric Matrices, it has been shown that every symmetric matrix A can be expressed as A = EΛE’ where E is a matrix whose columns are the eigenvectors of A with the normRead More

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