The probability distribution of a random variable X is given belo… - Vidyadip

MCQ

The probability distribution of a random variable X is given below.

X = k	0	1	2	3	4
P(X = k)	0.1	0.4	0.3	0.2	0

The variance of X is

A
1.6
B
0.24
✓
0.84
D
0.75

✓

Answer

Correct option: C.

0.84

(C)
$\mathrm{E}(\mathrm{X})=\sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}\right)$
$\begin{aligned}&=0(0.1)+1(0.4)+2(0.3)+3(0.2)+4(0) \\ &=0+0.4+0.6+0.6+0 \\ &=1.6 \\ & \text { Variance }=\mathrm{E}\left(\mathrm{X}^2\right)-[\mathrm{E}(\mathrm{X})]^2 \\ &= 0^2(0.1)+1^2(0.4)+2^2(0.3)+3^2(0.2)+4^2(0)-1.6^2 \\ &= 0+0.4+1.2+1.8-2.56 \\ &= 0.84\end{aligned}$

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