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Competitive Stats
Q30Section I (Objective (Q1–Q80))30 of 80

Probability — indicator variables and their algebraic identities

Consider two events A and B such that P(A)=1/4P(A) = 1/4, P(B∣A)=1/2P(B\mid A) = 1/2 and P(A∣B)=1/4P(A\mid B) = 1/4. Define random variable X as X=1X=1 if event A occurs and 0 if event A does not occur. Define random variable Y as Y=1Y=1 if event B occurs and 0 if event B does not occur. Then consider the following statements:

  1. P(X2+Y2=1)=1/4P(X^2+Y^2=1) = 1/4
  2. P(XY=X2Y2)=1P(XY = X^2Y^2) = 1

Which of the above statements is/are correct?

Options

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