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From Discrete to Continuous
A New World of Randomness
In Chapter 2, our random variables could only take countable values: 0, 1, 2, 3, ... (like counting heads or defects).
Now we enter the world of continuous random variables, where X can be any value in an interval.
Examples of Continuous Random Variables
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Time until a light bulb burns out (could be 1000.5 hours, 1000.51 hours, ...)
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Height of a randomly selected person (5.7 feet, 5.71 feet, ...)
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Temperature at a random time (72.3°F, 72.31°F, ...)
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Position where a dart lands on a number line
Key Difference: With continuous RVs, there are uncountably many possible values. You can always find another value between any two values!