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Probability Distributions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability Distributions2 Marks
MCQ
For a random variable $X$, if $E(X)=5$ and $\operatorname{Var}(X)=6$, then $E\left(X^2\right)$ is equal to
  • A
    19
  • ✓
    31
  • C
    61
  • D
    11
✓

Answer

Correct option: B.
31
(B)
$\begin{aligned} & \text {Since, } \operatorname{Var}(X)=E\left(X^2\right)-[E(X)]^2 \\ & \therefore \quad 6=E\left(X^2\right)-(5)^2 \\ & \therefore E\left(X^2\right)=25+6=31\end{aligned}$

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