 What Is the Importance of Probability and Probability Distributions?

It is crucial to note that random samples are not “perfect.” No two random samples will be the same because random samples are still at best random. One random sample may represent the population rather accurately, yet another random sample may be inaccurate, owing to chance alone. Unfortunately, while looking at a sample, we never know how much it differs from the population (which is what happens in practice).

In this position of ambiguity, we utilize probability to determine how much random samples are likely to vary.

Despite the uncertainty introduced by the use of a random sample, this allows us to draw inferences about the population.

Probability Distributions

Understanding probability distributions helps us to calculate the probability of a specific event while also accounting for its variability. As a result, we may infer from the sample to the entire population, estimate the data-generating function, and better forecast the behavior of a random variable.

Random Variables

In broad terms, a random variable is a numerical representation of the outcome of an experiment. A random variable can be either Discrete or Continuous.

Discrete and Continuous Probability Distributions

In probability, a discrete distribution has a finite or countably infinite number of possible values. That is, you can enumerate or list every conceivable value, such as 1, 2, 3, 4, 5, 6…100.

Examples of a discrete random variable include the number of students in a class, the number of people that go to Shoprite on a given date, test questions answered correctly, the number of children in a family, number of defective products in a batch in a manufacturing plant etc.

Also, a discrete probability distribution can be described using a table, graph, or equation.

Discrete probability distributions include discrete uniform, binomial, Poisson, geometric, negative binomial, and hypergeometric probability distributions.

Conversely, a random variable is continuous if any two of its values are separated by an infinite number of other valid values like 0.2, 82.88cm, 40.335 miles etc. Continuous random variables include things like pressure, the height of boys in a given class, mass, distance traveled, running time of an athlete, interest rate of loans

What is Uniform Probability Distribution, and how does it work?

In statistics, this refers to a form of probability distribution in which each possible outcome has an equal chance of occurring. The probability is constant since each variable has an equal chance of being the outcome.

Types of Uniform Probability Distribution

1. Continuous uniform distribution: This has an unlimited number of equally likely measurable values. An example of a continuous uniform distribution includes a random number generator.
2. Discrete uniform distribution: This has a limited number of equally like outcomes. Examples are the probability of head or tail when a coin is tossed, the probability of landing on any side of a die etc. Organizations can benefit from discrete uniform distribution in a variety of ways, including inventory management, raffle draws etc.

That’s all for now folks. See you in the next post where we would discuss some other types of probability distributions.

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