The probability distribution of \(X\) is as follows :\(x\)01234\(P[X = x]\)0.1\(k\)\(2k\)\(2k\)\(k\)Find (i) \(k\), (ii) \(P(X \lt 2)\), (iii) \(P[1 \le X \lt 4]\)

Q.25 The probability distribution of \(X\) is as follows :

\(x\)	0	1	2	3	4
\(P[X = x]\)	0.1	\(k\)	\(2k\)	\(2k\)	\(k\)

Find (i) \(k\), (ii) \(P(X \lt 2)\), (iii) \(P[1 \le X \lt 4]\)

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: (i) \(k = 0.15\) (ii) 0.25 (iii) 0.75

(i) \(\sum P(x) = 1\): \(0.1 + k + 2k + 2k + k = 1 \Rightarrow 6k = 0.9 \Rightarrow k = 0.15\).

(ii) \(P(X \lt 2) = P(0) + P(1) = 0.1 + 0.15 = 0.25\).

(iii) \(P(1 \le X \lt 4) = P(1) + P(2) + P(3) = k + 2k + 2k = 5k = 0.75\).

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

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