Understanding probability distribution

Let's look at an example where you draw a random sample and measuring the heights of the subjects. When you measure heights, you will have to create a distribution of heights. Such type of distribution will help you know the possible outcomes that you are most likely to obtain, how you can spread the potential values and how you are likely to get different results. We will also learn about probability distributions that put into considerations the continuous variable and the discrete variables.

Properties of a Probability Distribution

Here, we shall discuss more generally on the overall properties of probability distributions. As we had learned earlier, a probability distribution is a function that indicates how likely an event or outcome can occur. General features of the probability distribution are-

• A probability is denoted as p(x). This is likelihood that a particular random variable will take a specified value of x
• The total sum of all probabilities of possible values should or must equal to 1. Moreover, the likelihood of a specific range of values or single value must lie between 0 and 1.
• A different kind of variable determines a different type of probability. For example, in a single random variable, discrete variables determine discrete probability distributions. And for continuous variables, they determine probability density functions.
• A probability distribution is represented by either equations or tables of variable values.

Discrete Probability Distributions

Also known as probability mass functions, discrete probability functions assume a discrete number of values. Examples of these discrete functions are events counts and coin tosses. When you are counting the number of events, you only count as 1, 2… and when tossing a coin, the only outcomes are either heads or tails. In discrete distributions, there are no any in-between values.

The possible values in discrete probability distribution functions have non-zero likelihoods. However, all these possible values must add up to 1. Hence, a single value should occur for every opportunity. For example, when rolling a die, the probability of a specific number must be 1/6.

Types of Discrete Distributions

Depending on the properties of your data, there are vast types of discrete probability distributions that one can use when modeling his or her data. These discrete probability distributions include:

• Binomial distribution, e.g., Tossing of coin
• Poisson distribution, e.g., Counting of events
• Uniform distribution, e.g., Rolling of a die

Continuous Probability Distributions/Probability Density Functions

In a continuous probability distribution, the variables assume an infinite number of values between 2 values. These types of variables are measured on a scale. They include weight, height, and temperature.

In a continuous probability distribution, unlike in discrete probability distribution, the specific values have zero probability.

Types of Continuous Probability Distributions

There are three types of continuous probability distributions. Namely,

• Normal distribution
• Weibull distribution
• Lognormal distribution

All these types of continuous probability distributions can fit skewed data.

Need "Pay someone to do my homework" Services?

For further information on statistics assignment help, do not hesitate to contact us through our email and live chats. We professionally assure you of an original, quality, timely delivery and extensively researched online homework service.