Probability Essentials
Introduction Probability allows us to quantify the variability in the outcome of any experiment whose exact outcome cannot be predicted
Distributions, YES
Distributions
Describes the probability of outcomes for a random variable, defined by specific parameters and assumptions. Each capturing different real-world phenomena through precise mathematical models.
Distributions, YES
Transformation of Random Variables
Introduction In this note, we study how to find the probability distribution of functions of one or more random variables.
Distributions, YES
The Role of Parameters
Introduction In one of the previous notes, we discussed several common families of distributions. In this note, we discuss the
Distributions, YES
Expectation and Moments of Univariate Distributions
Introduction Random variable characterises a random phenomenon by listing the range and the corresponding probability distribution (that is, pmf in
Distributions, YES
Generating Functions in Random Variables
Introduction A random variable X is completly described by its CDF, PDF, or PMF. But summarizing a distribution would be
Distributions, YES
Properties of Univariate & Bivariate Distributions
Introduction We now prove several useful properties of the expectation of a random variable $X$, which is applied in univatiate
Distributions, YES
Expectation & Moments of Bivariate Distributions
Introduction Random variable characterises a random phenomenon by listing the range and the corresponding probability distribution (that is, pmf in
Distributions, YES
Bivariate Distributions
Introduction We generalise the concept of probability distribution of a random variable to the joint distribution of two random variables.
Distributions, YES
Random variable & Probability Function
Introduction Random variable and theoretical distributions play very important role in modeling uncertainty. It offers a syntactic approach for the
Distributions, YES
Theoretical Distributions
Introduction When we define a function in mathematics, it usually has a parameter — something that stays fixed for one