7 topics, 48 short and super clear episodes

This Probability theory course includes 48 short and super clear episodes that take 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.

## 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