Exploring basic and discrete probability distributions

A random variable of an event is denoted by X (capital) and its value is represented using x (small). Probability of event X is denoted as P(X). A sample space is the list of all the possible outcomes in a random experiment. Random variables can either be discrete variable which takes a specific value in a range while the continuous variable can take any value in the range provided. Normal probability distribution is an example of a continuous probability distribution function. The parameter can change the value of the output event in probability distributions. This effect is best illustrated when the distribution functions are graphed. When the probability function describes a discrete probability distribution, it is denoted as a probability mass function (pmf), and is written as P(X=x).

Summation of all the probabilities associated with all the possible numerical values is equal to one (1). Example In an experiment involving tossing of a coin P(t) + P(h) = 1 P(t)= 1/2 P(h)= 1/2 Where the symbol P(t) is used to denote the probability of the result being a T (tail) and P(h) is used to denote probability of the result being a head. All the trials are independent in other words, the results of one trial are not contingent on those of the preceding trial. Negative binomial probability distribution This distribution has a number of unique characteristics. There are a number of trials that are done repeatedly. The results of each trial can only be one of the two results, and the results are independent of each other.