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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 $\operatorname{Var}(X)=4$ and $\mathrm{E}\left(\mathrm{X}^2\right)=13$, the value of $\mathrm{E}(\mathrm{X})$ is
  • ✓
    3
  • B
    4
  • C
    5
  • D
    6
✓

Answer

Correct option: A.
3
(A)
$\begin{aligned} & \text {Since } \operatorname{Var}(X)=E\left(X^2\right)-[E(X)]^2 \\ & \therefore \quad 4=13-[E(X)]^2 \\ & \therefore \quad[E(X)]^2=13-4=9 \\ & \therefore \quad E(X)=3\end{aligned}$

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