Probabilities from a pdf by Integration (University)
Free printable university probability worksheet computing P(a < X < b) = F(b) - F(a) and E(X) by integrating simple polynomial and uniform pdfs, with exact symbolic answers cross-checked numerically.
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Probability & Statistics · Math worksheet
Name
Date
Math
Continuous Random Variables: Probabilities by Integration
Integrate each probability density function to find P(a < X < b) = F(b) - F(a), or the expected value E(X) = integral of x f(x). Round answers to 4 decimal places.
- 1.X has pdf f(x) = 14 for 3 <= x <= 7, and f(x) = 0 otherwise. Compute P(6 < X < 6.5) by integrating the pdf. Round to 4 decimal places.
- 2.X has pdf f(x) = 2x/36 for 0 <= x <= 6, and f(x) = 0 otherwise. Compute P(4.5 < X < 5.5) by integrating the pdf. Round to 4 decimal places.
- 3.X has pdf f(x) = 2(6 - x)/36 for 0 <= x <= 6, and f(x) = 0 otherwise. Compute P(1 < X < 6) by integrating the pdf. Round to 4 decimal places.
- 4.X has pdf f(x) = 2(3 - x)/9 for 0 <= x <= 3, and f(x) = 0 otherwise. Find E(X) by evaluating the integral of x f(x) over the support. Round to 4 decimal places if not exact.
- 5.X has pdf f(x) = 2x/9 for 0 <= x <= 3, and f(x) = 0 otherwise. Compute P(1 < X < 3) by integrating the pdf. Round to 4 decimal places.
- 6.X has pdf f(x) = 2x/25 for 0 <= x <= 5, and f(x) = 0 otherwise. Compute P(X > 4.5) by integrating the pdf. Round to 4 decimal places.
- 7.X has pdf f(x) = 2(4 - x)/16 for 0 <= x <= 4, and f(x) = 0 otherwise. Compute P(X > 1.5) by integrating the pdf. Round to 4 decimal places.
- 8.X has pdf f(x) = 2(4 - x)/16 for 0 <= x <= 4, and f(x) = 0 otherwise. Compute P(0 < X < 1.5) by integrating the pdf. Round to 4 decimal places.
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