random variable used frequently in probability and uncertainty measurementa random variable is basically variable that can take on various values at random these variables can be of discrete or continuous type in general probability distribution probability distribution is distribution or arrangement that depicts the likelihood of random variable or variables to take on each of its probable states there are usually two main types of distributions based on the variable being discrete or continuous probability mass function probability mass functionalso known as pmfis probability distribution over discrete random variables popular examples include the poisson and binomial distributions probability density function probability density functionalso known as pdfis probability distribution over continuous random variables popular examples include the normaluniformand student' distributions marginal probability the marginal probability rule is used when we already have the probability distribution for set of random variables and we want to compute the probability distribution for subset of these random variables for discrete random variableswe can define marginal probability as follows ap for continuous random variableswe can define it using the integration operation as follows op dy conditional probability the conditional probability rule is used when we want to determine the probability that an event is going to take placesuch that another event has already taken place this is mathematically represented as follows ( yp , (ythis tells us the conditional probability of xgiven that has already taken place