Let X=aZ+b, where Z is a standard normal random variable, and a,b are two…

GATE · 2025 · DA · Data Science & AI

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

  1. A.

    a = −2, b = 1

  2. B.

    a = 2, b = −1

  3. C.

    a = −2, b = −1

  4. D.

    a = 1, b = 1

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