There are certain important properties of the continuous probability distribution. Distribution plots (such as discrete distribution equivalent bar graphs) are usually smooth curves. The curve is explained by an equation or function known as f (y). This is the equation of probability density that also corresponds to p (y) used for discrete variables. The total area under the curve is 1. This relates to the probabilities that have a total equal to 1 in the event in case of discrete probabilities. Random variable is indicated by the area present under the curve from a to b value. To find a value from the curve, the area between values -1 and 0.5 is used. It is like adding probabilities to the mutually exclusive discrete probability distributions.
Continuous variables are present in continuous probability distributions and discrete variables are present in discrete probability distributions. These two probability distribution types differ in several different ways. The probability is zero when a certain random variable matches a certain value. For example, suppose a person has a probability distribution of steady growth for men. Take an example of men’s height continuous probability distribution. In this chart, it is shown that seventy inches height is shown by average men (half is to the right and half of the area of the curve is to the left). However, it is impossible to grasp the probability that a man will exactly measure 70 inches. Imagine measuring the height of the man who is 70 inches tall. A man cannot be exactly 70 inches. The height could be 69.9795589 inches or 70.1045 inches. The fact is that it is impossible to accurately measure a variable on a continuous scale and therefore, it is impossible to understand the possibility of accurate measurement with a continuous probability distribution made. The discrete probability distribution can be represented by a frequency distribution table. In the form of a frequency distribution table or another type of diagram, the discrete probability distributions are usually described. A continuous probability distribution is expressed by a formula (probability density function) that describes the distribution shape. Countless sets and actual line spacing can be represented by a continuous distribution table. They are represented by a cumulative distribution function. This special function can calculate various probability distributions. There are several examples of continuous probability distributions, including uniform, normal, and chi-square. To find the area between the curves that represents a continuous probability distribution, use the calculus, which can be very difficult. For some distributions, it is impossible to directly calculate the area, and special digital methods are required. There are certain conditions that the probability function must satisfy.
1. Random variable Y is a function of X. That is, y = f (x).
2. The y value is more than or equal to 0 for all x values.
3. The entire area below the function curve is 1.
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