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Then the probability mass function f(X=x) = P () The table could be created on the basis of a random variable and possible outcomes.Say, a random variable X is a real-valued function whose domain is the sample space of a random experiment. X is the random variable of the number of heads obtained. Based on these outcomes we can create a distribution table. The formula for the normal distribution is; This distribution is also called a discrete probability distribution, where the set of outcomes are discrete in nature.
For a closed interval, (a→b), the cumulative probability function can be defined as; P(a, then, In the case of a random variable X=b, we can define cumulative probability function as; In the case of Binomial distribution, as we know it is defined as the probability of mass or discrete random variable gives exactly some value.
This distribution is also called probability mass distribution and the function associated with it is called a probability mass function.
These are the things that get mathematicians excited.
However, probability theory is often useful in practice when we use probability distributions.
Probability mass function is basically defined for scalar or multivariate random variables whose domain is variant or discrete.
Let us discuss its formula: Suppose a random variable X and sample space S is defined as; X : S → A And A ∈ R, where R is a discrete random variable.
Also, these functions are used in terms of probability density functions for any given random variable.
In the case of Normal distribution, the function of a real-valued random variable X is the function given by; F(x) = P(X ≤ x) Where P shows the probability that the random variable X occurs on less than or equal to the value of x.
The possible result of a random experiment is called an outcome. With the help of these experiments or events, we can always create a probability pattern table in terms of variable and probabilities.
There are basically two types of probability distribution which are used for different purposes and various types of data generation process.