PROBABILITY AND THEIR DISTRIBUTIONS

Probability plays a large role in Statistics.  It is the foundation for hypothesis testing, and many other areas of society. There are many different probability distributions that are used frequently in many sectors. Below you will find types of probability, and commonly used probability distributions.  Both discrete and continuous probability distributions are addressed.

Types of Probability

In this section, the different types of probability will be defined with examples of how to find them.  Types of probability include theoretical (or classical), experimental (or empirical) and subjective probability.

Theoretical or Classical
Theoretic Probability of Playing Cards
Experimental or Empirical
Experimental Probability from Frequency Table
Subjective 
Law of Large Numbers
Discrete vs Continuous Random Variables
Probability from a Two-Way Table

Probability Rules

There are many different rules for probability, as well as many types. Currently, there are examples for probability that involves combinations.

Finding Prob. Involving Combinations
Finding Prob. Involving Combinations-TI-84
Finding Prob. Involving Combinations-TI-Nspire

Discrete Probability Distributions

In this section, we will look at how to create a discrete distribution, and some commonly used discrete distributions.  A discrete random variable is a variable that can be counted. It cannot contain any fractions or decimals, only counting numbers for the random variable x.  There are general discrete probability distributions, and then special cases. The videos in this section show how to work with general discrete probability distributions.  The graph of a discrete distribution is always a histogram. In the next section, we will look at a common discrete distribution which is the Binomial distribution. 

Creating a Discrete Distribution TI-Nspire
Creating a Discrete Prob. Distribution TI-84
Finding Probabilities from a Prob. Distribution
Mean, Variance, St. Deviation of Random Discrete Variables - TI-84
Mean, Variance, and St. Deviation Discrete Random Variable-TI-Nspire
Expected Value for a Prob. Distribution
Expected Value of a Prob. Distribution TI-84
Expected Value of a Prob. Distribution Nspire

Binomial Probability Distributions

In this section,we will look at the binomial distribution. In order to be binomial, the outcomes must be able to be classified as a success or a failure, the probability of success must be the same throughout, the events must be independent of each other, there must be a fixed number of trials, and the random variable x represents the possible number of successes in the experiment. An example of a binomial experiment would be rolling a die 10 times, and recording the number of 5's that are rolled. Binomial distributions are very commonly used discrete distributions.

Binomial Prob. TI-84
Binomial Prob. TI-Nspire
Binomial Prob. Distribution and Histogram in TI-84
Binomial Prob. Distribution in TI-Nspire
Mean, Variance, and St. Deviation for Binomial Distribution

Normal Distribution

The normal distribution is the most commonly used continuous distribution in Statistics. The normal distribution follows the empirical rule or the 68-95-99.7 rule. The normal distribution has a lot of uses in our society. The standard normal distribution allows us to compare different distributions with different scales. The random variable x would be converted to a z-score in order to use the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. Normal distributions can have any mean and any standard deviation.

Prob. for Normal Distribution -Z-table
Prob. for Normal Distribution-TI-84
Prob. for Normal Distribution-TI-Nspire
Finding z-score Corresponding
to Given Area - z-table
Find z-score Given Area : TI-84
Find z-score: TI-84
Find z-score Given Area - TI-Nspire
Find z-score TI-Nspire
Find X-Value for a Normal Distribution - TI-84

Central Limit Theorem

The central limit theorem states that if you start with a normally distributed population (any sample size), or if you have a sample that is at least 30, the sampling distribution of the sampling means will approach a normal model with mean equal to the population mean, and standard error equal to the population standard deviation divided by the square root of the sample size. The distribution of the sampling distribution of the sample proportions will also approach a normal model.

The Central Limit Theorem
Mean and Standard Error of Sampling Distribution of Sample Means
Finding Prob. of Means
in a Sampling Distribution
Finding Prob. of Means in a Sampling Distribution-TI-84
Finding Prob. of Means in a Sampling Distribution-TI-Nspire