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A *random variable* is variable that gets its value by some random, (stochastic) process. A random variable is usually denoted by a capital letter, and usually in italics.

We may for example have

*X*=the result after throwing a fair six sided die.*Y*=the number of red cars passing a certain crossing in one day.*Z*=the sum of the values of the card in a poker hand, (A=1,… K=12)*W*=2 + the result after throwing a fair six sided die.

The result of an experiment (that could be an actual experiment, or, say, a survey) is called an *outcome* of the experiment. If I throw a die, and get a six, then six is the outcome of the experiment.

The set of possible outcomes is called the *sample space* *sample space* of the random variable. For a ordinary fair dice the sample space is:

{1 ,2, 3, 4, 5, 6}

*X*=a random variable.

This is basically connected to a description of how to get the random value, as described above. We may for example use this to ask “what is the probability that *X*=6?”, i.e. what is the probability that outcome of throwing a die is 6? This is often written P(*X*=6)

*x*=an actual outcome.

We may for example ask what is P(*X*=*x*) , i.e, what is the probability that our random variable *X* has the value *x*. This is often used in formulas for the probability. If we for example would have an urn with marbles marked with numbers, four with a 1, three with a 2, two with a 3 and one with a 4, and *X* is the result of randomly selecting one marble (after replacement) then we have the formula

I.e. the probability to get say a 3 is (5-3)/10=2/10, just as expected.

Up a level : Probability and Statistics

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