7 topics, 48 short and super clear lessons

This Probability theory course includes 48 short and super clear lessons that lead you through 7 topics and help you navigate the bumpy roads of Probability theory. The casual style makes you feel like you are discussing some simple issue, such as cooking scrambled eggs.

Table of contents: 

The course consists of 7 sections: Events, probabilities and combinatorics, Total probability theorem and Bayes’ theorem, Distribution, distribution function, density function, Expected value and standard deviation, Markov’s and Chebyshev’s inequalities, Discrete and continuous distributions, Distributions of two random variables

COMBINATORICS

  • Permutation - The number of permutations on a set of n elements is given by n!
  • k-permutation of n - Number of permutations of k items chosen from n different items.
  • Combination -  How many ways can we choose k items out of n items?

 

EVENTS & PROBABILITIES

  • Events - Let's start with a very simple thing. We have a die, roll it once, and see what kind of events could occur. We may roll a 1.It's also possible, that we roll a 2. Then, it is also possible that before the die stops, a meteorite hits Earth and destroys the die, along with the entire human civilization. 
  • Independence - In probability theory, to say that two events are independent means that the occurrence of one does not affect the probability of the other.
  • Mutually exclusive events -  Two events are mutually exclusive if they cannot occur at the same time.
  • Conditional probability - A given B it answers the question of what chance does A have, if B definitely occurs.
  • Total probability theorem - This formula is a fundamental rule relating marginal probabilities to conditional probabilities.
  • Bayes-theorem - We use this theorem if we want to calculate the probability of an earlier event (Bk) in light of a later occurring event (A). 

 

DISTRIBUTION FUNCTION & DENSITY FUNCTION

  • Random variable - Random variables assign numbers to events.
  • Distribution function - The distribution function of random variable X, and it is denoted by F(x). F(x)=P(x<X) But, before we fall victims of a fatal mistake, let's make it clear that x and X are two totally different things. 
  • Density function - The way the density function works is that the probabilities are given by the areas below the curve. 

EXPECTED VALUE AND STANDARD DEVIATION

  • Expected value - We get the expected values by multiplying the values of X by their probabilities, and then sum these up.
  • Standard deviation - The standard deviation tells us how large the fluctuation is around the expected value.
  • Markov's inequality - Markov's inequality makes a very simple statement,namely, that it is not very likely that a random variable X would get a lot bigger than its expected value.
  • Chebyshev's inequality - The Chebyshev's inequality says the distance from the expected value cannot be too large. 

 

COMMON DISTRIBUTIONS

  • Binomial distribution - The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.
  • Hypergeometric distribution - The hypergeometric distribution is a discrete probability distribution that describes the probability of k defected in n draws, without replacement, from a finite population of size N containing exactly K defected.
  • Poisson distribution - The Poisson distribution with parameter >>lambda<< is the discrete probability distribution of the number of successes in a sequence of infinitely many yes/no experiments, where >>lambda<< is the expected value of success experiments.
  • Uniform distribution - The uniform distribution, is a distribution that has constant probability.
  • Exponential distribution - Distribution of distance or time.
  • Normal distribution - Distribution of quantities 

 

DISTRIBUTIONS WITH TWO RANDOM VARIABLES

 

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