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This document contains mathematical equations for calculating the probability (P(X)) of a random variable (X) being between 1 and 4 based on its probability density function (f(x)). The probability is calculated as the area under the curve of f(x) between 1 and 4 (1/4 * f(x) dx) plus the area from 4 to infinity (1/4 * f(x) dx), divided by the total area under f(x) from negative infinity to positive infinity. The example shown solves for P(X) between 1 and 4 and equals 3/4.
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Gate 2016 cepaperimathematicsq26
- 3. 𝑃 𝑋 = −∞ 1 𝑓 𝑥 𝑑𝑥 1 4 𝑓 𝑥 𝑑𝑥 + 4 +∞ 𝑓 𝑥 𝑑𝑥
- 4. 𝑃 𝑋 = −∞ 1 𝑓 𝑥 𝑑𝑥 1 4 𝑓 𝑥 𝑑𝑥 + 4 +∞ 𝑓 𝑥 𝑑𝑥
- 5. 𝑃 𝑋 = −∞ 1 𝑓 𝑥 𝑑𝑥 1 4 𝑓 𝑥 𝑑𝑥 + 4 +∞ 𝑓 𝑥 𝑑𝑥 P(X) =0.25(𝑥)| 4 1 =3/4
- 6. 𝑃 𝑋 = −∞ 1 𝑓 𝑥 𝑑𝑥 1 4 𝑓 𝑥 𝑑𝑥 + 4 +∞ 𝑓 𝑥 𝑑𝑥 P(X) =0.25(𝑥)| 4 1 =3/4