Probability+Distribution

Go back HOME     Probability Distribution - introduction
 * **variable** - a symbol that represents a specific value
 * **statistical experiments** - outcome of statistical experiment is a random variable
 * <span style="font-family: Verdana,Geneva,sans-serif;">For an event to be a statistical experiment, the outcome of the event has to have more than one possibility, have probability involved, and have predictable results.
 * <span style="font-family: 'Comic Sans MS',cursive;"><span style="font-family: Verdana,Geneva,sans-serif;">Rolling a die is a statistical experiment because there are 6 possible outcomes, 1/6 probability of getting each number, and the result is one of 6 numbers
 * <span style="font-family: 'Comic Sans MS',cursive;"><span style="font-family: Verdana,Geneva,sans-serif;">**discrete** **variable** - random variables that are in intervals

<span style="font-family: Verdana,Geneva,sans-serif;">Different topics related to probability distribution
 * <span style="font-family: 'Comic Sans MS',cursive;"><span style="font-family: Verdana,Geneva,sans-serif;">cumulative probability distribution (click here to learn about cumulative probability distribution)
 * <span style="font-family: 'Comic Sans MS',cursive;"><span style="font-family: Verdana,Geneva,sans-serif;">uniform probability distribution (click here to learn about uniform probability distribution)
 * <span style="font-family: 'Comic Sans MS',cursive;"><span style="font-family: Verdana,Geneva,sans-serif;">normal distribution (click here to learn about normal distribution)

<span style="font-family: 'Comic Sans MS',cursive;"><span style="font-family: Verdana,Geneva,sans-serif;">Probability distribution in general is a representation of statistical experiment outcome (x variable ) and the probability of that outcome through a graph or an equation.

The x variable is a possible **number of occurrences** in an experiment p(x) is the probability that outcome defined by x will happen

In a simple statistical experiment of double coin toss, there are 4 possible outcomes with 1/4 probabilities (HH, HT, TH, TT).
 * The experiment yields
 * 1 two heads toss at 1/4 probability (2 heads in total)
 * 2 one head and one tail toss at 1/2 probability (1 head in total)
 * 1 two tails toss at 1/4 probability (0 head in total)

Now if we define x as number of times head appears in a toss, and p(x) represents the probability, then the experiment can be represented this way.


 * Number of heads occurrences ||  Probability  ||
 * 0 ||  0.25  ||
 * 1 ||  0.5  ||
 * 2 ||  0.25  ||

The table represents probability distribution of double coin toss where **x is discrete random variable**.

Graphed versions of probability distribution

Discrete Probability Graph Note how the independent values (1, 3, and 7) are in integers, not decimals. p(1) = 0.2 p(3) = 0.5 p(7) = 0.3

Any values not 1, 3, or 7 have probability of 0 (values such as decimals)

Sources & extra links for more information:
 * [|Statistic Tutorial: Statistic Experiments]
 * [|Statistic Tutorial: Probability Distribution]
 * [|Statistic Glossary]
 * [|Wikipedia: Discrete Probability Distribution]