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 ...

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