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Problem 13 - Entrance Test

A random variable X on {1,2,3,4} has E[X]=2.5 and Var(X)=1.25. What is P(X=2)?

Correct: B

Let probabilities be p₁,p₂,p₃,p₄. Solve Σp=1, Σxp=2.5, Σx²p–6.25=1.25. System yields p₂=0.25.