For the random variable dependent on one another requires the calculation of conditional probabilities which we already discussed, now we will discuss some more parameters for such random variables or experiments like conditional expectation and conditional variance for different types of random variables. Conditional Expectation The definition of conditional probability mass function of discrete…

# Mathematics

## Moment Generating Functions: 13 Important Facts

Moment generating function Moment generating function is very important function which generates the moments of random variable which involve mean, standard deviation and variance etc., so with the help of moment generating function only, we can find basic moments as well as higher moments, In this article we will see moment generating functions for the…

## Covariance, Variance Of Sums: 7 Important Facts

COVARIANCE, VARIANCE OF SUMS, AND CORRELATIONS OF RANDOM VARIABLES The statistical parameters of the random variables of different nature using the definition of expectation of random variable is easy to obtain and understand, in the following we will find some parameters with the help of mathematical expectation of random variable. Moments of the number…

## Conditional Variance & Predictions: 7 Important Facts

In this article the conditional Variance and predictions using conditional expectation for the different kind of random variable with some examples we will discuss. Conditional Variance The conditional variance of random variable X given Y is defined in similar way as conditional Expectation of random variable X given Y as (X|Y)=E[(X-E[X|Y])2|Y] here variance is the…

## 11 Facts On Mathematical Expectation & Random Variable

Mathematical Expectation and random variable The mathematical expectation plays very important role in the probability theory, the basic definition and basic properties of mathematical expectation already we discussed in previous some articles now after discussing the various distributions and types of distributions, in the following article we will get familiar with some more advanced properties…

## Conditional Distribution: 7 Interesting Facts To Know

ContentConditional distributionDiscrete conditional distributionExample on discrete conditional distributionContinuous conditional distributionExample on Continuous conditional distributionConditional distribution of bivariate normal distributionJoint Probability distribution of function of random variablesExamples on Joint Probability distribution of function of random variables Conditional distribution It is very interesting to discuss the conditional case of distribution when two random variables follows the…

## Jointly Distributed Random Variables: 11 Important Facts

Content Jointly distributed random variablesJoint distribution function | Joint Cumulative probability distribution function | joint probability mass function | joint probability density functionExamples on Joint distributionIndependent random variables and joint distributionExample of independent joint distributionSUMS OF INDEPENDENT RANDOM VARIABLES BY JOINT DISTRIBUTIONsum of independent exponential random variablessum of independent Gamma random variablessum of independent exponential…

## Gamma Distribution Exponential Family: 21 Important Facts

Content Special form of Gamma distributions and relationships of Gamma distribution Gamma distribution exponential family Relationship between gamma and normal distribution Poisson gamma distribution | poisson gamma distribution negative binomial Weibull gamma distribution Application of gamma distribution in real life | gamma distribution uses | application of gamma distribution in statistics Beta gamma distribution |…

## Inverse Gamma Distribution: 21 Important Facts

Inverse gamma distribution and moment generating function of gamma distribution In continuation with gamma distribution we will see the concept of inverse gamma distribution and moment generating function, measure of central tendencies mean, mode and median of gamma distribution by following some of the basic properties of gamma distribution. gamma distribution properties Some of the…

## Gamma Distribution: 7 Important Properties You Should Know

Gamma Distribution One of the continuous random variable and continuous distribution is the Gamma distribution, As we know the continuous random variable deals with the continuous values or intervals so is the Gamma distribution with specific probability density function and probability mass function, in the successive discussion we discuss in detail the concept, properties and…