Practice question · Fill in the blanks
Complete the statement about a continuous random variable X.
For a continuous random variable, the probability P(X = 3) equals ______.
Word bank: 0 · the density evaluated at 3 · 1 · an undefined quantity
Hints
- Probability for a continuous variable is an area under the density.
- What is the area of a region with zero width?
Show the answer
For a continuous random variable, the probability P(X = 3) equals 0.
Why
A single point has no width, so it encloses no area and carries no probability. The density value at 3 is generally positive but it is a density, not a probability, and it can even exceed 1. Only intervals carry probability here.
Practise Random Variables and Distributions
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