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

A random variable X has the following probability distribution :\(x\)1234567\(P(x)\)\(k\)\(2k\)\(2k\)\(3k\)\(k^2\)\(2k^2\)\(7k^2 + k\)Find (a) \(k\) (b) \(P(X \lt 3)\) (c) \(P(X \gt 6)\)

Q.5 (B)(iii) A random variable X has the following probability distribution :

\(x\)	1	2	3	4	5	6	7
\(P(x)\)	\(k\)	\(2k\)	\(2k\)	\(3k\)	\(k^2\)	\(2k^2\)	\(7k^2 + k\)

Find (a) \(k\) (b) \(P(X \lt 3)\) (c) \(P(X \gt 6)\)

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

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Answer: (a) \(k = \dfrac{1}{10}\) (b) \(P(X \lt 3) = 0.3\) (c) \(P(X \gt 6) = 0.17\)

(a) \(\sum P(x) = 1\): \(k + 2k + 2k + 3k + k^2 + 2k^2 + 7k^2 + k = 1 \Rightarrow 10k^2 + 9k - 1 = 0 \Rightarrow (10k - 1)(k + 1) = 0\). Since \(k \ge 0\), \(k = \dfrac{1}{10}\).

(b) \(P(X \lt 3) = P(1) + P(2) = k + 2k = 3k = \dfrac{3}{10} = 0.3\).

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

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A random variable X has the following probability distribution :\(x\)1234567\(P(x)\)\(k\)\(2k\)\(2k\)\(3k\)\(k^2\)\(2k^2\)\(7k^2 + k\)Find (a) \(k\) (b) \(P(X \lt 3)\) (c) \(P(X \gt 6)\)

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