CUET · MATHS · PYQ PAPER 2025
A random variable X has the following probability distribution :
| X | 0 | 1 | 2 | 3 |
| P(X) | 0.1 | 0.2 | 0.3 | 0.4 |
- A 1
- B 2
- C 2.3
- D 1.2
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(E[X] = \sum x P(x) = (0)(0.1) + (1)(0.2) + (2)(0.3) + (3)(0.4) = 0 + 0.2 + 0.6 + 1.2 = 2.0\) \(E[X^2] = \sum x^2 P(x) = (0^2)(0.1) + (1^2)(0.2) + (2^2)(0.3) + (3^2)(0.4) = 0 + 0.2 + 1.2 + 3.6 = 5.0\) \(Var(X) = E[X^2] - (E[X])^2 = 5.0 - (2.0)^2 = 5.0 - 4.0 = 1.0\)
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