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Question
If X ~ B(n, p) with n = 10, p = 0.4, then find E(X2).
Solution
For X ~ B(n, p), E(X) = np and V(X) = npq
Given that n = 10 and p = 0.4
∴ q = 1 – p
= 1 – 0.4
= 0.6
∴ E(X) = np
= 10 × 0.4
= 4
and
V(X) = npq
= 10 × 0.4 × 0.6
= 2.4
Also, V(X) = E(X2) – [E(X)]2
∴ 2.4 = E(X2) – (4)2
∴ E(X2) = 2.4 + 16
∴ E(X2) = 18.4
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