CUET · MATHS · PYQ PAPER 2025
A die is tossed once. If the random variable X is defined as \(\mathbf{X}=\left\{\begin{array}{ll}1, & \text { if the die result in an odd number } \\ -1, & \text { if the die result in an even number }\end{array}\right.\) then the variance of X is
- A 0
- B 1
- C \(\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
\(P(X=1) = \frac{3}{6} = \frac{1}{2}\) \(P(X=-1) = \frac{3}{6} = \frac{1}{2}\) \(E[X] = 1(\frac{1}{2}) + (-1)(\frac{1}{2}) = 0\) \(E[X^2] = (1)^2(\frac{1}{2}) + (-1)^2(\frac{1}{2}) = \frac{1}{2} + \frac{1}{2} = 1\) \(Var(X) = E[X^2] - (E[X])^2 = 1 - (0)^2 = 1\)
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