Q.26 If the p.m.f. of r.v. X be P(X = x) = ⁴C_x(5/9)^x(4/9)^(4-x) for x = 0, 1, 2, 3, 4 ; = 0 otherwise, then find E(X) and Var(X) .

Answer: E(X) = 20/9 , Var(X) = 80/81 The p.m.f. is that of a binomial distribution with n = 4 , p = 5/9 , q = 4/9 . E(X) = np = 4×5/9 = 20/9 . Var(X) = npq = 4×5/9×4/9 = 80/81 .

If the p.m.f. of r.v. \(X\) be \(P(X = x) = {}^4C_x\left(\frac{5}{9}\right)^x\left(\frac{4}{9}\right)^{4-x}\) for \(x = 0, 1, 2, 3, 4\); \(= 0\) otherwise, then find \(E(X)\) and \(\mathrm{Var}(X)\).

Q.26 If the p.m.f. of r.v. \(X\) be \(P(X = x) = {}^4C_x\left(\frac{5}{9}\right)^x\left(\frac{4}{9}\right)^{4-x}\) for \(x = 0, 1, 2, 3, 4\); \(= 0\) otherwise, then find \(E(X)\) and \(\mathrm{Var}(X)\).

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

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Answer: \(E(X) = \frac{20}{9}\), \(\mathrm{Var}(X) = \frac{80}{81}\)

The p.m.f. is that of a binomial distribution with \(n = 4\), \(p = \frac{5}{9}\), \(q = \frac{4}{9}\).

\(E(X) = np = 4\times\frac{5}{9} = \frac{20}{9}\).

\(\mathrm{Var}(X) = npq = 4\times\frac{5}{9}\times\frac{4}{9} = \frac{80}{81}\).

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

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If the p.m.f. of r.v. \(X\) be \(P(X = x) = {}^4C_x\left(\frac{5}{9}\right)^x\left(\frac{4}{9}\right)^{4-x}\) for \(x = 0, 1, 2, 3, 4\); \(= 0\) otherwise, then find \(E(X)\) and \(\mathrm{Var}(X)\).

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