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Module 1: Discrete random variables

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XSIQ
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Intermediate Mathematics - Random variables

Random variables

A random variable [1] is a variable whose value is a numerical outcome of
some random experiment. [2] An experiment is random if the outcome is
uncertain. For example, an experiment could be the random selection of a
male from a group of students (probability Height 180), or the selection
of a mussel from a catch made in order to measure the lead content, or the
toss of a coin, or the rolling of a die in a board game or the selection of
a card from a deck of cards. For example, with a group of male students
three different boys might have heights of 195 cm, 184 cm and 178cm. A
random variable has an unknown value before the experiment and an observed
numerical value after the experiment. Random variables are denoted by a
capital letter, such as X, Y and Z. The observed values are denoted by the
corresponding lower case letters, x, y, and z.

For example, when a die is rolled, let the random variable, X, be the
number on the face which is uppermost when the die comes to rest. There are
only 6 possible values for X : 1, 2, 3, 4, 5 or 6. X cannot take values
like 1.72 or 3.268. Thus X is a discrete random variable.

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[2] http://alison.com/#