Practice question · Multiple choice
For a continuous random variable, P(X = 3) = 0 for every single value - yet X certainly takes SOME value. How can every individual outcome have probability zero?
Hints
- For a continuous variable, how is probability computed - by summing masses, or by taking an area?
- What is the area of a region with zero width?
Show the answer
B. Because probability is area under a density, and a point has none.
Why
For a continuous variable probability is area under a density, and the area over a region of zero width is zero, so P(X = 3) = 0 while P(2.9 < X < 3.1) is positive. The probability is exactly zero rather than merely small, which is why a probability-zero event is not an impossible one, and why 'exactly 180 cm' is not a question the model answers.
Practise Random Variables and Distributions
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More questions on Random Variables and Distributions
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