Find E(X) and V(X), where X is the number obtained on uppermost face, when a fair die is thrown.

Question 88 of 88

E(X)

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2026Subjective· 3mImportance★★★★★

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$X$ is uniform on $\{1,2,3,4,5,6\}$ each with probability $1/6$ ; use $E(X)$ and $E(X^2)$ .

Probability distribution: $P(X=x)=\dfrac16$ for $x=1,2,3,4,5,6$ .

$E(X)=\sum x\cdot P(X=x)=\frac{1+2+3+4+5+6}{6}=\frac{21}{6}=\frac72$

$E(X^2)=\frac{1^2+2^2+3^2+4^2+5^2+6^2}{6}=\frac{1+4+9+16+25+36}{6}=\frac{91}{6}$

$V(X)=E(X^2)-[E(X)]^2=\frac{91}{6}-\left(\frac72\right)^2=\frac{91}{6}-\frac{49}{4}$

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Q.Find $E(X)$ and $V(X)$ , where $X$ is the number obtained on uppermost face, when a fair die is thrown.