what is discrete distribution 
a discrete distribution is a probability distribution that depicts the occurrence of discrete individually countable outcomes such as 1 2 3 yes no true or false the binomial distribution for example is a discrete distribution that evaluates the probability of a yes or no outcome occurring over a given number of trials given the event s probability in each trial such as flipping a coin one hundred times and having the outcome be heads statistical distributions can be either discrete or continuous a continuous distribution is built from outcomes that fall on a continuum such as all numbers greater than 0 including numbers whose decimals continue indefinitely such as pi 3 14159265 overall the concepts of discrete and continuous probability distributions and the random variables they describe are the underpinnings of probability theory and statistical analysis understanding discrete distributiondistribution is a statistical concept used in data research those seeking to identify the outcomes and probabilities of a particular study will chart measurable data points from a data set resulting in a probability distribution diagram many probability distribution diagram shapes can result from a distribution study such as the normal distribution bell curve statisticians can identify the development of either a discrete or continuous distribution by the nature of the outcomes to be measured unlike the normal distribution which is continuous and accounts for any possible outcome along the number line a discrete distribution is constructed from data that can only follow a finite or discrete set of outcomes discrete distributions thus represent data with a countable number of outcomes meaning that the potential outcomes can be put into a list and then graphed the list may be finite or infinite for example when determining the probability distribution of a die with six numbered sides the list is 1 2 3 4 5 6 if you re rolling two dice the chances of rolling two sixes 12 or two ones two are much less than other combinations on a graph you d see the probabilities of the two represented by the smallest bars on the chart types of discrete probability distributionsthe most common discrete probability distributions include binomial bernoulli multinomial and poisson 1a binomial probability distribution is one in which there is only a probability of two outcomes in this distribution data are collected in one of two forms after repetitive trials and classified into either success or failure it generally has a finite set of just two possible outcomes such as zero or one for instance flipping a coin gives you the list heads tails the binomial distribution is used in options pricing models that rely on binomial trees in a binomial tree model the underlying asset can only be worth exactly one of two possible values with the model there are just two probable outcomes with each iteration a move up or a move down with defined values bernoulli distributions are similar to binomial distributions because there are two possible outcomes one trial is conducted so the outcomes in a bernoulli distribution are labeled as either a zero or one a one indicates success and a zero means failure one trial is called a bernoulli trial so if you used one green marble for success and one red marble for failure in a covered bowl and chose without looking you would record each result as a zero or one rather than success or failure for your sample bernoulli distributions are used to view the probability that an investment will succeed or fail multinomial distributions occur when there is a probability of more than two outcomes with multiple counts for instance say you have a covered bowl with one green one red and one yellow marble for your test you record the number of times you randomly choose each of the marbles for your sample in finance and investing these distributions estimate the probability that a specific set of financial events will occur the poisson distribution expresses the probability that a given number of events will occur over a fixed period the poisson distribution is a discrete distribution that counts the frequency of occurrences as integers whose list 0 1 2 can be infinite for instance say you have a covered bowl with one red and one green marble and your chosen period is two minutes your test is to record whether you pick the green or red marble with the green indicating success after each test you place the marble back in the bowl and record the results in this model the distribution would be plotting the results over a period of time indicating how often green is chosen poisson distribution is commonly used to model financial data where the tally is small and often zero for example it can be used to model the number of trades a typical investor will make in a given day which can be 0 often 1 2 and so on discrete distributions can also be seen in the monte carlo simulation a monte carlo simulation is a modeling technique that identifies the probabilities of different outcomes through programmed technology it is primarily used to help forecast scenarios and identify risks in a monte carlo simulation outcomes with discrete values will produce discrete distributions for analysis these distributions determine risk and trade offs among different items being considered calculation of discrete probability distribution