Surfstat.australia: an online text in introductory Statistics

VARIATION AND PROBABILITY

RANDOM VARIABLES

A random variable (r.v.) is a numerical value which is defined on or determined by the outcomes or events of an experiment. Random variables are usually denoted by capital letters, X, Y etc and can be discrete or continuous.

Let the r.v. X be the number of seeds germinating from 100. Possible values for X are 0,1,2,100, (discrete)

Let the r.v. X be the maximum daily temperature in Newcastle. Possible values are 0 - 50 C e.g. 26.1276(continuous).

Let X be response to question with 'Yes', 'No', 'Don't know'. X is not a r.v. (not numerical).

Let Y be number of 'Yes's. Y is discrete r.v.

Probability Distribution of a Discrete r.v.

This is a list of the possible values of the r.v. and the corresponding probabilities (which must sum to 1). The probabilities may be written:

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