MHT CET · Maths · Probability
For the probability distribution of X given below
The variance of \(X\) is
- A \(2.4257\)
- B \(2.5427\)
- C \(2.5742\)
- D \(2.2475\)
Answer & Solution
Correct Answer
(D) \(2.2475\)
Step-by-step Solution
Detailed explanation
\(\sum_{i=1}^{n} x_{i} P_{i}=E(X)\)
\(E(X) =(-2)(0.2)+(-1)(0.3)+0(0.1)+1(0.15)\) \(+~2(0.25) \)
\( =-0.4-0.3+0.15+0.50=-0.7+0.65=-0.05 \)
\( E\left(X^{2}\right) =\sum_{i=1}^{n} x_{i}^{2} P_{i} \)
\( =4(0.2)+1(0.3)+0(0.1)+1(0.15)+4(0.25) \)
\( =0.8+0.3+0.15+1=2.25 \)
\( =E\left(X^{2}\right)-[E(X)]^{2} \)
\( =2.25-0.0025=2.2475\)
\(E(X) =(-2)(0.2)+(-1)(0.3)+0(0.1)+1(0.15)\) \(+~2(0.25) \)
\( =-0.4-0.3+0.15+0.50=-0.7+0.65=-0.05 \)
\( E\left(X^{2}\right) =\sum_{i=1}^{n} x_{i}^{2} P_{i} \)
\( =4(0.2)+1(0.3)+0(0.1)+1(0.15)+4(0.25) \)
\( =0.8+0.3+0.15+1=2.25 \)
\( =E\left(X^{2}\right)-[E(X)]^{2} \)
\( =2.25-0.0025=2.2475\)
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