Core - Statistics

Chapter 6

Probability Distributions

6.1 : Probability in Statistics

6.1 : Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when ...

6.2 : Random Variables

6.2 : Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability ...

6.3 : Probability Distributions

6.3 : Probability Distributions

The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a ...

6.4 : Probability Histograms

6.4 : Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of ...

6.5 : Unusual Results

6.5 : Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In ...

6.6 : Expected Value

6.6 : Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would ...

6.7 : Binomial Probability Distribution

6.7 : Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes. The ...

6.8 : Poisson Probability Distribution

6.8 : Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of ...

6.9 : Uniform Distribution

6.9 : Uniform Distribution

The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular. Two ...

6.10 : Normal Distribution

6.10 : Normal Distribution

The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in ...

6.11 : <em>z</em> Scores and Area Under the Curve

6.11 : z Scores and Area Under the Curve

z scores are the standardized values obtained after converting a normal distribution into a standard normal distribution. A z score is measured in units ...

6.12 : Applications of Normal Distribution

6.12 : Applications of Normal Distribution

The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal ...

6.13 : Sampling Distribution

6.13 : Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each ...

6.14 : Central Limit Theorem

6.14 : Central Limit Theorem

The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample ...

Copyright © 2025 MyJoVE Corporation. Alle Rechte vorbehalten