<p>\(X \sim B(10, 0.4)\). The value of \(E(X^2)\) is <em>[JEE Advanced 2015]</em></p>
Step-by-Step Solution
Key Concept: E(X^2) = Var(X) + [E(X)]^2. For Bin(10,0.4): E(X)=4, Var(X)=2.4. So E(X^2) = 2.4+16 = 18.4.
<p>$E(X) = np = 10 \times 0.4 = 4$.</p><p>$\text{Var}(X) = np(1-p) = 10 \times 0.4 \times 0.6 = 2.4$.</p><p>$E(X^2) = \text{Var}(X) + [E(X)]^2 = 2.4 + 16 = 18.4$.</p><p>Given answer key C. Specific option value from original: 18.4 or 184/10.</p>
Correct Answer: C