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Chapter 6

Probability Distributions

Probability in Statistics
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 ...
Random Variables
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 ...
Probability Distributions
Probability Distributions
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a ...
Probability Histograms
Probability Histograms
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of ...
Unusual Results
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 ...
Expected Value
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 ...
Binomial Probability Distribution
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 ...
Poisson Probability Distribution
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 ...
Uniform Distribution
Uniform Distribution
The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular. Two ...
Normal Distribution
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 ...
<em>z</em> Scores and Area Under the Curve
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 ...
Applications of Normal Distribution
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 ...
Sampling Distribution
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 ...
Central Limit Theorem
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 ...
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