Chi-square table

What is Probability Distribution?

In Probability Distribution, A Random Variable’s outcome is uncertain. Here, the outcome’s observation is known as Realization. It is a Function that maps Sample Space into a Real number space, known as State Space. They can be Discrete or Continuous....

Random Variables

Random Variable is a real-valued function whose domain is the sample space of the random experiment. It is represented as X(sample space) = Real number....

Types of Random Variables in Probability Distribution

There are following two types of...

Probability Distribution of a Random Variable

Now the question comes, how to describe the behavior of a random variable?...

Probability Distribution Formulas

The various formulas under Probability Distribution are tabulated below:...

Expectation (Mean) and Variance of a Random Variable

Suppose we have a probability experiment we are performing, and we have defined some random variable(R.V.) according to our needs( like we did in some previous examples). Now, each time experiment is performed, our R.V. takes on a different value. But we want to know that if we keep on doing the experiment a thousand times or an infinite number of times, what will be the average value of the random variable?...

Different Types of Probability Distributions

We have seen what Probability Distributions are, now we will see different types of Probability Distributions. The Probability Distribution’s type is determined by the type of random variable. There are two types of Probability Distributions:...

Discrete Probability Distributions

Discrete Probability Functions also called Binomial Distribution assume a discrete number of values. For example, coin tosses and counts of events are discrete functions. These are discrete distributions because there are no in-between values. We can either have heads or tails in a coin toss....

Cumulative Probability Distribution

The Cumulative Probability Distribution for continuous variables is a function that gives the probability that a random variable takes on a value less than or equal to a specified point. It’s denoted as F(x), where x represents a specific value of the random variable. For continuous variables, F(x) is found by integrating the probability density function (pdf) from negative infinity to x. The function ranges from 0 to 1, is non-decreasing, and right-continuous. It’s essential for computing probabilities, determining percentiles, and understanding the behavior of continuous random variables in various fields....

Probability Distribution Function

Probability Distribution Function is defined as the function that is used to express the distribution of a probability. Different types of probability, they are expressed differently. These functions are also used for Probability Density Functions for different variables....

Probability Distribution Table

The random variables and their corresponding probability is tabulated then it is called Probability Distribution Table. The following table represents a Probability Distribution Table:...

Prior Probability

Prior Probability as the name suggests refers to assigning the probability of an event before the happening of a dependent event that makes us make changes in the Prior Probability. Let’s say we assign Probability P(A) to event A before taking into account that event B has also happened. After B has happened we need to revise P(A) using Baye’s Theorem. Hence, here P(A) is the Prior Probability. If we predict that a particular observation will fall into a particular category before collecting all the observations, then this is also called Prior Probability....

Posterior Probability

After the Prior Probability has been assigned and new information is obtained then the Prior Probability is modified by taking into account the newly obtained information using Baye’s Formula. This revised probability is called Posterior Probability. Hence, we can say that Posterior Probability is a conditional probability obtained by revising the Prior Probability....

Chi-square distribution

Chi-square distribution is a probability distribution that arises in statistics, particularly in hypothesis testing and confidence interval estimation. It is characterized by its degrees of freedom, which determine its shape. The distribution is positively skewed and only takes non-negative values. The Chi-square distribution is widely used in inferential statistics for testing the independence of variables in contingency tables, assessing goodness of fit, and estimating population variances....

Chi-square table

Below is a Chi-square table showing critical values for selected degrees of freedom and levels of significance:...

t Distribution

The t distribution, also known as the Student’s t-distribution, is a probability distribution that is similar to the standard normal distribution but has heavier tails. It is commonly used in hypothesis testing and constructing confidence intervals when the sample size is small or the population standard deviation is unknown. The shape of the t distribution depends on the sample size, and as the sample size increases, the t distribution approaches the standard normal distribution....

t Table

Below is a t-table showing critical values for selected degrees of freedom (df) and levels of significance:...

Solved Questions on Probability Distribution

Question 1: A box contains 4 blue balls and 3 green balls. Find the probability distribution of the number of green balls in a random draw of 3 balls....

Conclusion – Probability Distribution

In conclusion, a probability distribution serves as a theoretical model of how likely various outcomes are to occur. While a frequency distribution deals with observed data, detailing the occurrences of different values within a sample, a probability distribution assigns probabilities to each possible outcome, reflecting the likelihood of encountering those values....

FAQs on Probability Distribution

What is Probability Distribution in statistics?...