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Explain the concept of a random variable in mathematics.
Explain the concept of a random variable in mathematics.
A random variable is a mathematical formalization of a quantity or object which depends on random events. It is a function from possible outcomes in a sample space to a measurable space, often to the real numbers.
Why is the term 'random variable' considered misleading?
Why is the term 'random variable' considered misleading?
The term 'random variable' is considered misleading because its mathematical definition is not actually random nor a variable. It is a function from possible outcomes in a sample space to a measurable space.
What does the term 'randomness' typically represent in the context of random variables?
What does the term 'randomness' typically represent in the context of random variables?
Informally, randomness typically represents some fundamental element of chance, such as in the roll of a die; it may also represent uncertainty, such as measurement error.
What does a random variable map possible outcomes to?
What does a random variable map possible outcomes to?
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In what way does the interpretation of probability become philosophically complicated?
In what way does the interpretation of probability become philosophically complicated?
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