Q.4 (C)(iii) Given p.d.f. of a continuous random variable X is, f(x) = x/8, for 0 lt x lt 4; = 0, otherwise. Then P(1 lt x lt 2) = ____.

Answer: 3/16 displaystyle P(1 lt X lt 2) = ∫₁² x/8 dx = 1/8[x²/2]₁² = 1/16(4 - 1) = 3/16.

Chapter: Probability Distributions· Mathematics & Statistics (Commerce) Part 2

Given p.d.f. of a continuous random variable \(X\) is, \(f(x) = \dfrac{x}{8}\), for \(0 \lt x \lt 4\); \(= 0\), otherwise. Then \(P(1 \lt x \lt 2) =\) ____.

Q.4 (C)(iii) Given p.d.f. of a continuous random variable \(X\) is, \(f(x) = \dfrac{x}{8}\), for \(0 \lt x \lt 4\); \(= 0\), otherwise. Then \(P(1 \lt x \lt 2) =\) ____.

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: \(\dfrac{3}{16}\)

\(\displaystyle P(1 \lt X \lt 2) = \int_1^2 \frac{x}{8}\,dx = \frac{1}{8}\left[\frac{x^2}{2}\right]_1^2 = \frac{1}{16}(4 - 1) = \frac{3}{16}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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Given p.d.f. of a continuous random variable \(X\) is, \(f(x) = \dfrac{x}{8}\), for \(0 \lt x \lt 4\); \(= 0\), otherwise. Then \(P(1 \lt x \lt 2) =\) ____.

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