Probability distribution tables

Introduction to Probability Distribution Tables

• A probability distribution table provides a summary of the possible outcomes of a statistical experiment, along with the associated probabilities.
• The xi column (random variable outcomes) represents the possible outcomes of the random variable.
• The P(X=xi) column provides the probabilities associated with each of these outcomes.

Properties of Probability Distribution Tables

• All probabilities in the table must be between 0 and 1, inclusive. This reflects the fact that a probability cannot be less than 0% (impossible) or more than 100% (certain).
• The sum of all probabilities in the table must equal 1. This indicates that one of the listed outcomes will definitely occur.

Constructing Probability Distribution Tables

• Generally, a probability distribution table is constructed after conducting an experiment or survey and collecting data.
• To assign probabilities, count the number of times each outcome occurs and divide by the total number of outcomes.
• Ensure that all probabilities in the table add up to 1, adjusting if necessary to account for rounding errors.

Reading and Using Probability Distribution Tables

• Use the table to find the probability of a specific outcome or a set of outcomes. Add together the probabilities of the individual outcomes to find the total probability.
• Often used to calculate expected values, the mean (average), variance (spread), or other statistics of a random variable.

Further Points

• Probability distribution tables are closely related to probability trees, and you can often construct one from the other.
• They’re a key tool for answering probability questions in the Further Stats 1 part of the maths Further Maths syllabus.
• A deep understanding of these tables is essential for tackling more complex statistical topics.