Gate DA 2025 | Question - 11 | Probability and Statistics

July 15, 2025

Suppose X and Y are random variables. The conditional expectation of X given Y is denoted by $E [X | Y]$ . Then $E [E [X | Y]]$ equals

$E [X | Y]$

$\frac{E [X]}{E [Y]}$

$E [X]$

$E [Y]$

Solution:

It is about the law of iterated expectations, also known as the tower property of conditional expectation. It states:

$E [E [X ∣ Y]] = E [X]$

This law holds regardless of the dependence between $X$ and $Y$ .

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