Q.6 (A) (iii) The following is the p.d.f. of a r.v. X : f(x)=x/8 for 0lt xlt 4 ; =0 , otherwise. Find (a) P(xlt 1.5) (b) P(1lt xlt 2) (c) P(xgt 2)

Answer: (a) 9/64 (b) 3/16 (c) 3/4 For 0lt alt blt 4 : ∫_a^bx/8 dx=[x²/16]_a^b=b²-a²/16 . (a) P(xlt 1.5)=∫₀^(1.5)x/8 dx=2.25/16=9/64≈ 0.1406 (b) P(1lt xlt 2)=4-1/16=3/16 (c) P(xgt 2)=∫₂⁴x/8 dx=16-4/16=3/4

The following is the p.d.f. of a r.v. X : \(f(x)=\frac{x}{8}\) for \(0\lt x\lt 4\); \(=0\), otherwise.Find (a) \(P(x\lt 1.5)\) (b) \(P(1\lt x\lt 2)\) (c) \(P(x\gt 2)\)

Q.6 (A) (iii) The following is the p.d.f. of a r.v. X : \(f(x)=\frac{x}{8}\) for \(0\lt x\lt 4\); \(=0\), otherwise.

Find (a) \(P(x\lt 1.5)\) (b) \(P(1\lt x\lt 2)\) (c) \(P(x\gt 2)\)

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: (a) \(\frac{9}{64}\) (b) \(\frac{3}{16}\) (c) \(\frac{3}{4}\)

For \(0\lt a\lt b\lt 4\): \(\int_a^b\frac{x}{8}\,dx=\left[\frac{x^2}{16}\right]_a^b=\frac{b^2-a^2}{16}\).

(a) \(P(x\lt 1.5)=\int_0^{1.5}\frac{x}{8}\,dx=\frac{2.25}{16}=\frac{9}{64}\approx 0.1406\)

(b) \(P(1\lt x\lt 2)=\frac{4-1}{16}=\frac{3}{16}\)

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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The following is the p.d.f. of a r.v. X : \(f(x)=\frac{x}{8}\) for \(0\lt x\lt 4\); \(=0\), otherwise.Find (a) \(P(x\lt 1.5)\) (b) \(P(1\lt x\lt 2)\) (c) \(P(x\gt 2)\)

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