The random variable X can take values 0, 1, 2. If P(X=0)=P(X=1)=, and E(X^2)=E(X), then which of the following are correct? (A) E(X) = 2-3 (B) E(X^2) = 4+7 (C) = 1/2 (D) = 1/5 Choose the **correct** answer from the options given below: Option 1: (A), (B) and (C) only Option 2: (A), (C) and (D) only Option 3: (B) and (C) only Option 4: (A) and (C) only

The answer is '(A) and (C) only'. View full solution:

Algebra > Probability

Medium

applied

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$, and $E(X^2)=E(X)$, then which of the following are correct? (A) $E(X) = 2-3\alpha$ (B) $E(X^2) = 4+7\alpha$ (C) $\alpha = \frac{1}{2}$ (D) $\alpha = \frac{1}{5}$ Choose the correct answer from the options given below:

(A), (B) and (C) only

(A), (C) and (D) only

(B) and (C) only

(A) and (C) only

✅ Correct Option: 4

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The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$, and $E(X^2)=E(X)$, then which of the following are correct? (A) $E(X) = 2-3\alpha$ (B) $E(X^2) = 4+7\alpha$ (C) $\alpha = \frac{1}{2}$ (D) $\alpha = \frac{1}{5}$ Choose the correct answer from the options given below: