Types Of Distribution In Statistics | Probability Distribution Explained | Statistics | Simplilearn

This paragraph introduces the concept of probability distribution, explaining it as a list of all possible outcomes of a random variable along with their corresponding probability values. It highlights the importance of this concept in various fields and introduces the three main types of distributions: normal, binomial, and Poisson. The normal distribution is described as a continuous probability density function that results in a symmetrical bell curve, often observed in data that clusters around a central value without bias to the left or right. An example of height distribution in a class is given to illustrate this concept, showing how the average height is the most common and likelihood decreases as one moves away from the average in either direction.

This section delves into the concept of standard deviation, which measures the dispersion of a dataset relative to its mean. It explains how a higher standard deviation indicates a more spread out dataset, using the example of income disparities between rural and urban areas. The paragraph also describes how to calculate standard deviation through the process of finding the squared average of the differences between each data point and the mean. Furthermore, it introduces the standard normal distribution, a specific type of normal distribution with a mean of zero and a standard deviation of one, and explains its properties, including the proportion of values falling within certain standard deviation intervals.

The paragraph discusses the properties of the standard normal distribution that facilitate easy calculations, such as the percentage of values falling within specific standard deviation intervals. It then introduces the concept of the Z-score, which measures how many standard deviations an individual data point is from the mean. The Z-score is calculated by subtracting the mean from the data point and dividing by the standard deviation. The paragraph provides an example using daily travel time data to demonstrate how to calculate the mean, standard deviation, and Z-score, explaining the significance of these values in understanding data distribution.

This section covers fundamental probability terms such as outcomes, random experiments, events, and sample space. It defines an outcome as the result of a random experiment, like flipping a coin or rolling a die, and a random experiment as a well-defined procedure with an unpredictable outcome. The concept of sample space is introduced as the set of all possible outcomes of a random experiment. Additionally, the paragraph explains the difference between discrete and continuous random variables, providing an example of a discrete random variable representing the sum of numbers when two dice are rolled.

The final paragraph introduces two specific types of probability distributions: binomial and Poisson. The binomial distribution is used for experiments with exactly two outcomes, success and failure, and is calculated using a specific formula involving the binomial coefficient. The paragraph outlines the conditions for a binomial experiment and provides an example involving the tossing of a die. In contrast, the Poisson distribution is used for counting the number of events likely to happen over a given period of time at a constant rate. It is used in scenarios where the probability of an individual event is very small. The paragraph concludes with an example of how to calculate the Poisson distribution and poses a problem for the audience to solve involving the arrival of trains at a station.