Table of Contents
What is the Probability Distribution?
The probability distribution is a mathematical function that assigns a probability to each outcome of an event. The function can be represented by a table, graph, or formula. The most common type of probability distribution is the normal distribution.
Probability Distribution of Random Variables
A probability distribution is a mathematical function that assigns a probability to each value that a random variable can take on.
For discrete random variables, the probability distribution is a table that lists the probabilities for each value the random variable can take on.
For continuous random variables, the probability distribution is a graph that shows the relative likelihood of the random variable taking on any given value.
Probability Distribution Definition
A probability distribution is a mathematical function that assigns a probability to each possible outcome of an event. The function can be used to calculate the probability of any event by using the values of the function at the points corresponding to the outcomes.
A probability distribution can be discrete or continuous. A discrete probability distribution has a finite number of outcomes, while a continuous probability distribution has an infinite number of outcomes.
Types of Probability Distribution:
1. Binomial Distribution
2. Poisson Distribution
3. Normal Distribution
4. Exponential Distribution
5. Chi-squared Distribution
6. Weibull Distribution
These Two Types of Probability Distribution are:
1. Binomial Distribution
2. Normal Distribution
Normal Probability Distribution
A normal probability distribution is a type of probability distribution in which the likelihood of any given outcome is determined by a normal distribution curve. In a normal distribution curve, the most likely outcome falls in the middle of the curve, and the likelihood of any given outcome decreases as the distance from the center of the curve increases.
Binomial / Discrete Probability Distribution
A binomial probability distribution is a discrete probability distribution that describes the probability of a certain number of successes in a sequence of n independent Bernoulli trials.
Negative Binomial Distribution
The negative binomial distribution is a discrete probability distribution that is used to model the number of failures that occur before a particular number of successes is achieved. It is a variation of the binomial distribution, and is parameterized by the number of successes (k) and the number of failures (n).
Poisson Probability Distribution
A Poisson distribution is a discrete probability distribution that models the probability of a given number of events occurring in a given interval of time. The Poisson distribution is often used to model the number of events that occur in a given time period.
PRIOR Probability of Success
1.0
0.5
0.25
0.1
0.05
0.01
Probability Distribution Formulas
The formulas for the most common types of probability distributions are listed below.
Normal Distribution
\(p(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{x^2}{2\sigma^2}}\)
Student’s t Distribution
\(p(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\)
Binomial Distribution
\(p(x) = \frac{x}{n}p^{x}(1-p)^{n-x}\)
Poisson Distribution
\(p(x) = \frac{e^{-\lambda}}{x!}\)
Probability Distribution Function
P(x) =
1/2 for x ≤ 1
3/8 for 1 < x ≤ 2
1/4 for 2 < x ≤ 3
1/8 for 3 < x ≤ 4 0 for x > 4
Probability Distribution Table Introduction
A probability distribution table is used to help organize and understand the probabilities of different outcomes in a given scenario. In a probability distribution table, each row corresponds to a different outcome, and each column corresponds to a different probability. The table is typically filled in by calculating the probabilities of different outcomes, and then organizing them in a table.
There are a few different types of probability distribution tables. The most common type is the binomial distribution table. This type of table is used to calculate the probabilities of different outcomes in a binomial distribution. A binomial distribution is a type of probability distribution that is used to calculate the probabilities of different outcomes in a scenario where there are only two possible outcomes, and the chances of each outcome are the same.
Another type of probability distribution table is the normal distribution table. This type of table is used to calculate the probabilities of different outcomes in a normal distribution. A normal distribution is a type of probability distribution that is used to calculate the probabilities of different outcomes in a scenario where the outcomes are all normally distributed.
Probability Distribution Table Example
Suppose that you are interested in calculating the probabilities of different outcomes in a binomial distribution. To do this, you can use a binomial distribution table.
In a binomial distribution table, each row corresponds to a different outcome, and each column corresponds to a different probability. The table is typically filled in by calculating the probabilities of different outcomes, and then organizing them
Probability Distribution Table
A probability distribution table is a table that shows the probability of each possible outcome of an event.
Solved Example
Problem:
A company has 10,000 shares of common stock outstanding. The company has a net income of $120,000 and paid a cash dividend of $6,000.
What is the company’s earnings per share?
Earnings per share = Net Income / Number of Shares Outstanding = $120,000 / 10,000 = $12.00
