Probability Distribution (Discrete & Continuous)
Probability Distribution (Discrete & Continuous)
A probability distribution is a mathematical function that describes the probability of different possible values of a variable. In other words, it is a way of expressing how likely it is for a variable to take on a certain value. Probability distributions can be used to model a wide variety of phenomena, such as the outcome of a coin toss, the height of a person, or the return on an investment.
There are two main types of probability distributions: discrete and continuous. Discrete distributions are used to model variables that can only take on a limited number of values. For example, the probability distribution for the outcome of a coin toss is discrete, because it can only be heads or tails. Continuous distributions are used to model variables that can take on an infinite number of values. For example, the probability distribution for the height of a person is continuous, because a person can be any height between 0 and 8 feet tall.
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1. Random Variables & Discrete Probability Distribution | #randomvariables #maths
2. Cumulative Distribution Function - Discrete | Probability Distribution #randomvariables #maths
Subscribe my YouTube Channel for all the videosIn probability theory and statistics, a continuous probability distribution is a probability distribution that describes the probability of the values of a continuous random variable. In contrast to discrete probability distributions, a continuous probability distribution is defined over an interval of possible values, rather than a countable set of possible values. Continuous probability distributions are used to model a wide variety of phenomena, including the heights of people, the weights of animals, and the time it takes for a light bulb to burn out. They are also used in many areas of mathematics and statistics, such as calculus, linear algebra, and machine learning.
Subscribe my YouTube Channel for all the videosThe moment generating function (MGF) is a function that describes the distribution of a random variable. It is defined as the expected value of an exponential function. The MGF can be used to determine the probability distribution of a variable at every point. The MGF encodes all the moments of a random variable into a single function. Moments describe the location, size, and shape of a probability density function. The MGF allows us to calculate these moments using derivatives, which are easier to work with than integrals. If two random variables have the same MGF, then they must have the same distribution.
10. Poisson Distribution | Random Variables | Probability Distribution #probabilitydistribution #maths
The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson (/ˈpwɑːsɒn/; French pronunciation: [pwasɔ̃]). The Poisson distribution can be used to describe a wide variety of phenomena, such as the number of phone calls received by a switchboard in a given hour, the number of customers arriving at a store in a given minute, or the number of errors in a given piece of DNA. The Poisson distribution has several properties that make it useful for modeling data. First, it is relatively easy to calculate. The probability of observing a particular number of events can be calculated using a simple formula. Second, the Poisson distribution is very flexible. It can be used to model data that is distributed in a variety of ways. Finally, the Poisson distribution is well-understood. There is a large body of research on the Poisson distribution, which makes it possible to use it effectively to model data. The Poisson distribution is a powerful tool that can be used to model a wide variety of phenomena. It is relatively easy to calculate, flexible, and well-understood. As a result, it is one of the most widely used probability distributions in statistics.
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