Let \(x\) and \(y\) be random variables, not necessarily independent, that…

GATE · 2024 · CS · Set 2 · Computer Science & IT

Let xx and yy be random variables, not necessarily independent, that take real values in the interval [0,1]. Let 𝑧=𝑥𝑦𝑧 = 𝑥𝑦 and let the mean values of 𝑥,𝑦,𝑧𝑥, 𝑦, 𝑧 be x‾,y‾,z‾\overline {x}, \overline {y}, \overline {z}, respectively. Which one of the following statements is TRUE?

  1. A.

    z‾=x‾y‾ \overline {z} = \overline {x} \overline {y}

  2. B.

    z‾≤x‾y‾ \overline {z} \leq \overline {x} \overline {y}

  3. C.

    z‾≥x‾y‾ \overline {z} \geq \overline {x} \overline {y}

  4. D.

    z‾≤x‾ \overline {z} \leq \overline {x}

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