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Discrete and Continuous Probability Distributions

Discrete and Continuous Probability Distributions

1.   Theory of Discrete and Continuous Probability Distributions

In Statistics, probability distributions are those which assume values which are variable can take at random and which is shown by two functions, namely discrete and continuous probability distributions. The discrete function supports the values which are finite or those that can be counted, while continuous function holds good for those values which are infinite or cannot be counted.  The range of values can be plotted on a probability distribution curve and it assumes a maximum value along with a minimum value which determines the position of any value on the graph based on certain criteria like standard deviation and the mean value of the distribution which is indicated in the graph.

For any business purpose, mainly discrete probability distributions are utilized and they are of several types namely, binomial, which confines to two possible outcomes as a result of probability trails, Poisson, where time frame is involved in calculating the number of times an event may occur and geometric, which measures the number of trials before the outcome of the first success. 

While Continuous distribution is of two types, namely, uniform and normal distributions, in which uniform distributions determine the continuous arrival of any product depending on the time interval.  The normal distribution is the widely used probability distribution with its popular bell shaped curve, under which all probabilities are distributed.  Here, medium categories occur the maximum number of times, while extremes of values occur minimally which is characteristic of the normal curve. For example, if heights and weights of several individuals are presented in the form of Normal Probability Distribution, it will assume a bell shaped curve. 

Even for stocks, probability distributions are used, namely to indicate the returns from shares, in terms of negative and positive values, which represents some skewing from the normal distribution. In risk management conditions probability distributions are used to evaluate the extent of gains and losses through a probability distribution curve which determines whether investment in such a financial portfolio will be feasible or not. 

The concept of cumulative probability is the possibility of a collection of random variables, for example, the chances for a coin to fall heads if it is flipped twice, where the two times represent cumulative probability. Cumulative probability can be denoted by either graph or through tabular representation where the probability of occurrence is generally less than the number of times of occurrences. 

Uniform probability distribution is one type in which the variables involved in the probability are all similar in nature resulting in an equal probability. This usually occurs in case of ages of children in particular grades or when there is same level of pricing opted for several commodities, say for example, some items being priced at $ 10 in a low price shop. 

Thus probability is of much practical use and has several applications in business and statistical concepts. 

2.   Problems encountered in solutions to Discrete and Continuous Probability Distributions problems

The major problem arising in calculation of probability distributions is the way in which the variables have to be considered. The types of probabilities will also be confusing for the students and the way in which they should be solved should be clearly understood before initiating the solutions.

In probabilities involving risk management, the students should be familiar with how to tackle investing in values which are at risk. This requires meticulous planning as such investments might lead to greater losses. Therefore, students should be aware of the probabilities of gaining and then advice on investments in such risk management portfolios.

Certain types of continuous data could only be represented in the Normal Distribution or bell-shaped curve and the students should be aware of the fact the discrete data cannot be represented. Even in a bell shaped curve, some errors might occur if the correct values are not included in the calculations.

Students might make errors of judgment in cumulative probability where there is accumulation of values.  Care should be taken while expressing the values in either graphical form or tabular form as there might be some discrepancies while cumulating the values and the final calculation might go erroneous.

All these discrepancies will create a feeling in the minds of the students that Probability Distributions are laborious to work out and strenuous in nature.  However, these myths could be overcome by obtaining suitable assistance from experienced hands.

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