CUET · MATHS · PYQ PAPER 2025
The random variable \(X\) can take values 0, 1, 2 . If \(P(X=0)=P(X=1)=\alpha\), and \(E\left(X^2\right)=E(X)\), then which of the following are correct?
\(E(X)=2-3 \alpha\)
\(E\left(X^2\right)=4+7 \alpha\)
\(\alpha=\frac{1}{2}\)
\(\alpha=\frac{1}{5}\)
Choose the correct answer from the options given below :
- A (A), (B) and (C) only
- B (A), (C) and (D) only
- C (B) and (C) only
- D (A) and (C) only
Answer & Solution
Correct Answer
(D) (A) and (C) only
Step-by-step Solution
Detailed explanation
\(P(X=2) = 1 - \alpha - \alpha = 1 - 2\alpha\) \(E(X) = (0)\alpha + (1)\alpha + (2)(1-2\alpha)\) \(E(X) = \alpha + 2 - 4\alpha = 2 - 3\alpha\) \(E(X^2) = (0^2)\alpha + (1^2)\alpha + (2^2)(1-2\alpha)\) \(E(X^2) = \alpha + 4(1 - 2\alpha) = \alpha + 4 - 8\alpha = 4 - 7\alpha\)…
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