GATE 2014 EE (EE2) – Question 37
X has density $f(x)=0.2$ for |x| ≤ 1, 0.1 for 1 < |x| ≤ 4, and zero otherwise. Find P(0.5 < X < 5).
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Correct answer: 0.35 to 0.45
Explanation
The interval0.5to1has density0.2and contributes0.5×0.2=0.1. The interval1to4has density0.1and contributes3×0.1=0.3. There is no density above4,so total probability is **0.4**. The density is continuous-distribution data,so endpoint inclusion has no effect.