Question

explain continuous probablity distrubutions and give an example of distribution and bell-shaped distribution.

Answer 1

A continuous probability distribution is a probability distribution with a cumulative distribution function that is absolutely continuous. Equivalently, it is a probability distribution on the real numbers that is absolutely continuous with respect to Lebesgue measure. Such distributions can be represented by their probability density functions. If the distribution of X is continuous, then X is called a continuous random variable. There are many examples of continuous probability distributions: normal, uniform, chi-squared, and others.

Formally, if X is a continuous random variable, then it has a probability density function ƒ(x), and therefore its probability of falling into a given interval, say [a, b], is given by the integral

In particular, the probability for X to take any single value a (that is a ≤ X ≤ a) is zero, because an integral with coinciding upper and lower limits is always equal to zero.

Example of continuous distribution

One such probability distribution is Uniform continuous distribution.

The continuous uniform distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.

Example of a bell shaped distribution.

In probability theory  normal distribution is a type of continuous probability distribution for a real valued random variable. The general form of its probability density function is

all the curves here are of normal distribution with different parameters. And all the curve are bell shaped curve.