MHT CET · Maths · Probability
The probability distribution of a random variable X is given by
Then the variance of X is
- A 1.76
- B 2.45
- C 3.2
- D 4.8
Answer & Solution
Correct Answer
(A) 1.76
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \mathrm{E}(\mathrm{X})= & \sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}\right) \\ = & 0(0.4)+1(0.3)+2(0.1)+3(0.1)+4(0.1) \\ = & 1.2 \\ \operatorname{Var}(\mathrm{X}) & =\mathrm{E}\left(\mathrm{X}^2\right)-[\mathrm{E}(\mathrm{X})]^2 \\ & =0^2(0.4)+1^2(0.3)+2^2(0.1)+3^2(0.1) \\ & +4^2(0.1)-(1.2)^2 \\ & =0.3+0.4+0.9+1.6-1.44 \\ & =1.76\end{aligned}\)
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