MHT CET · Maths · Probability
If \(\mathrm{P}(\mathrm{X}=2)=0.3, \mathrm{P}(\mathrm{X}=3)=0.4, \mathrm{P}(\mathrm{X}=4)=0.3\), then the variance of random variable X is
- A 1.6
- B 6.6
- C 3.6
- D 0.6
Answer & Solution
Correct Answer
(D) 0.6
Step-by-step Solution
Detailed explanation
Given probability distribution is
\(\mathrm{E}(\mathrm{X})=\sum x_{\mathrm{i}} \mathrm{P}\left(x_{\mathrm{i}}\right) \)
\(=2(0.3)+3(0.4)+4(0.3) \)
\( \mathrm{E}(\mathrm{X}) =3 \)
\( \text {Variance } =\mathrm{E}\left(x^2\right)-[\mathrm{E}(x)]^2 \)
\( =2^2(0.3)+3^2(0.4)+4^2(0.3)-(3)^2 \)
\( =0.6\)
\(\mathrm{E}(\mathrm{X})=\sum x_{\mathrm{i}} \mathrm{P}\left(x_{\mathrm{i}}\right) \)
\(=2(0.3)+3(0.4)+4(0.3) \)
\( \mathrm{E}(\mathrm{X}) =3 \)
\( \text {Variance } =\mathrm{E}\left(x^2\right)-[\mathrm{E}(x)]^2 \)
\( =2^2(0.3)+3^2(0.4)+4^2(0.3)-(3)^2 \)
\( =0.6\)
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