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GATE DA 2025 Set 1 — Question 20

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MCQ+1 / -0.33MediumStandard NormalContinuous Random VariablesProbability & StatisticsExpectation (Continuous)Variance (Continuous)

Probability & Statistics → Continuous Random Variables → Expectation (Continuous)

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Question

Let X=aZ+bX = aZ + b, where ZZ is a standard normal random variable, and a,ba, b are two unknown constants. It is given thatE[X]=1,E[(X−E[X])Z]=−2,E[(X−E[X])2]=4,E[X] = 1, \quad E[(X - E[X])Z] = -2, \quad E[(X - E[X])^2] = 4,where E[X]E[X] denotes the expectation of random variable XX. The values of a,ba, b are:
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