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The probability distribution of a random variable XX is

x0123
P(X = x)14\frac{1}{4}18\frac{1}{8}18\frac{1}{8}12\frac{1}{2}

The variance of XX is

Solution

✅ Correct Option: 3

E(X)=0⋅14+1⋅18+2⋅18+3⋅12=158E(X) = 0 \cdot \frac{1}{4} + 1 \cdot \frac{1}{8} + 2 \cdot \frac{1}{8} + 3 \cdot \frac{1}{2} = \frac{15}{8}. E(X2)=0+1⋅18+4⋅18+9⋅12=418E(X^2) = 0 + 1 \cdot \frac{1}{8} + 4 \cdot \frac{1}{8} + 9 \cdot \frac{1}{2} = \frac{41}{8}. Variance =E(X2)−(E(X))2=418−22564=328−22564=10364= E(X^2) - (E(X))^2 = \frac{41}{8} - \frac{225}{64} = \frac{328 - 225}{64} = \frac{103}{64}.

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