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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.
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