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2026 PEA Q12

If X∼Bernoulli(p)X \sim \text{Bernoulli}(p), then E(X2)E(X^2) equals

Reveal answer and solution

Answer

B

Solution

  1. 1

    Since X∈{0,1}X \in \{0,1\}, we have X2=XX^2 = X, hence E(X2)=E(X)=pE(X^2) = E(X) = p.

Answer structure / marking notes

Note Var⁡(X)=p(1−p)=E(X2)−(EX)2\operatorname{Var}(X) = p(1-p) = E(X^2) - (E X)^2.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2026/ISI_MSQE_PEA_2026_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.