What is continuous distribution?

A continuous distribution describes the possibilities of the possible values of endless variate . endless variate may be a variate with a group of possible values (known because the range) that’s infinite and uncountable.

Probabilities of continuous random variables (X) are defined because the area under the curve of its PDF. Thus, only ranges of values can have a nonzero probability. The probability that endless variate equals some value is usually zero.

Example of the distribution of weights


The continuous Gaussian distribution can describe the distribution of weight of adult males. For instance , you’ll calculate the probability that a person weighs between 160 and 170 pounds.

Distribution plot of the load of adult males

The shaded region under the curve during this example represents the range from 160 and 170 pounds. the world of this range is 0.136; therefore, the probability that a randomly selected man weighs between 160 and 170 pounds is 13.6%. The whole area under the curve equals 1.0.

However, the probability that X is strictly adequate to some value is usually zero because the world under the curve at one point, which has no width, is zero. For instance , the probability that a person weighs exactly 190 pounds to infinite precision is zero. You’ll calculate a nonzero probability that a person weighs quite 190 pounds, or but 190 pounds, or between 189.9 and 190.1 pounds, but the probability that he weighs exactly 190 pounds is zero.

What is a discrete distribution?

A discrete distribution describes the probability of occurrence of every value of a discrete variate . A discrete variate may be a variate that has countable values, like an inventory of non-negative integers.

With a discrete probability distribution, each possible value of the discrete variate are often related to a non-zero probability. Thus, a discrete probability distribution is usually presented in tabular form.

Example of the amount of customer complaints

With a discrete distribution, unlike with endless distribution, you’ll calculate the probability that X is strictly adequate to some value. For instance , you’ll use the discrete Poisson distribution to explain the amount of customer complaints within each day . Suppose the typical number of complaints per day is 10 and you would like to understand the probability of receiving 5, 10, and 15 customer complaints during a day.

x P (X = x)

5 0.037833

10 0.125110

15 0.034718