Find the expected value, variance and standard deviation of r.v. \(X\) whose p.m.f. is given as :\(X=x\)123\(P(X)\)\(\frac15\)\(\frac25\)\(\frac25\)

Q.26 Find the expected value, variance and standard deviation of r.v. \(X\) whose p.m.f. is given as :

\(X=x\)	1	2	3
\(P(X)\)	\(\frac15\)	\(\frac25\)	\(\frac25\)

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

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Answer: \(E(X)=2.2\), \(Var(X)=0.56\), \(\sigma\approx0.75\)

\(E(X)=\sum x_ip_i=1\cdot\dfrac15+2\cdot\dfrac25+3\cdot\dfrac25=\dfrac{1+4+6}{5}=\dfrac{11}{5}=2.2\).

\(E(X^2)=\sum x_i^2p_i=\dfrac15+\dfrac85+\dfrac{18}5=\dfrac{27}{5}=5.4\).

\(Var(X)=E(X^2)-[E(X)]^2=5.4-4.84=0.56\).

\(\sigma=\sqrt{0.56}\approx0.7483\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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