Applications of Integrals · Centroids & Averages
Probability (Continuous)
For a continuous random variable with probability density function f(x), the probability that X falls between a and b is the integral of f from a to b.
- 0 variables
- 2 worked examples
- 14 in Applications of Integrals
Worked examples
If f(x) = 2x on [0, 1] (and 0 elsewhere), find P(0.25 ≤ X ≤ 0.75).
- ∫₀.₂₅^0.75 2x dx = [x²]₀.₂₅^0.75 = 0.5625 - 0.0625 = 0.5
Answer: 0.5 (50%)
1 more worked examplePremium
A waiting time has density f(x) = 2e^(-2x) for x ≥ 0. Find P(X ≥ 1).
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