A random variable X has the following probability distribution: X… - Vidyadip

MCQ

A random variable X has the following probability distribution:

$\mathrm{X}=x_i$	1	2	3	4
P($\mathrm{X}=x_i$)	0.1	0.2	0.3	0.4

The mean and the standard deviation are respectively

A
3 and 2
✓
3 and 1
C
3 and $\sqrt{3}$
D
2 and 1

✓

Answer

Correct option: B.

3 and 1

(B)
Mean $=\mathrm{E}(\mathrm{X})=\sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}\right)$
$=1(0.1)+2(0.2)+3(0.3)+4(0.4)=3$
$\begin{aligned}& \operatorname{Var}(\mathrm{X})=\mathrm{E}\left(\mathrm{X}^2\right)-[\mathrm{E}(\mathrm{X})]^2 \\& =1^2(0.1)+2^2(0.2)+3^2(0.3)+4^2(0.4)-(3)^2 \\& =0.1+0.8+2.7+6.4-9=10-9=1\end{aligned}$
$\therefore \quad$ S.D. $=1$

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