Probability and Probability Distributions – MathandStatsHelp

Probability Rules

In this section, we will look at several types of general probability rules. Bayes rule is a common rule used in Statistics to a find a probability when given a prior even occurring. Videos also cover example of "and" and "or" probability rules. When working with "and" probabilities, you must first determine if the events are independent (the probability of the first event doesn't change the probability of the second event.) Both "and" probability rules for independent and dependent events will be discussed. I will also demonstrate the different "or" probability rules. If the events cannot occur at the same time, they use a different rule than if the can occur at the same time.

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.

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.

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.

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.