You find the values of a random variable by observing the variable, but understand that you have one realization of the random variable — you haven’t captured the full distribution.
The name random variable is really an oxymoron. Random variables are neither random nor are they variables. A random variable is a (Borel-measureable) function from a sample space into (the real) numbers. If you don’t understand the phrases in parentheses, don’t worry. The key idea is this: there is a sample space (where things happen) and a random variable is a function that maps values from the sample space into a set of numbers.
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Usually simply by asking yourself what could possibly happen.
If you are considering the result of spinning a spinner, look at the spinner.
If you are considering the number of goals in a football match, then the random variable must be a non-negative integer. There is no obvious upper limit, but, in practice, an upper limit of 99 should work.
If you are considering the number of years between eruptions of a volcano, then the random variable must be a positive real number. Again, there is no obvious upper limit, but, in practice, you may impose an upper limit of 999, on the basis that anything more than 999 years in the future is of no interest to your readers.
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Answer:
You find the values of a random variable by observing the variable, but understand that you have one realization of the random variable — you haven’t captured the full distribution.
The name random variable is really an oxymoron. Random variables are neither random nor are they variables. A random variable is a (Borel-measureable) function from a sample space into (the real) numbers. If you don’t understand the phrases in parentheses, don’t worry. The key idea is this: there is a sample space (where things happen) and a random variable is a function that maps values from the sample space into a set of numbers.
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Usually simply by asking yourself what could possibly happen.
If you are considering the result of spinning a spinner, look at the spinner.
If you are considering the number of goals in a football match, then the random variable must be a non-negative integer. There is no obvious upper limit, but, in practice, an upper limit of 99 should work.
If you are considering the number of years between eruptions of a volcano, then the random variable must be a positive real number. Again, there is no obvious upper limit, but, in practice, you may impose an upper limit of 999, on the basis that anything more than 999 years in the future is of no interest to your readers.
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