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GATE DA 2026 Q63: Correlation of X and Y when Y depends on X²

Question

Let XX be a random variable that follows Uniform(−1,1)Uniform(-1, 1) distribution. The conditional distribution of the random variable YY given X=xX = x is the Uniform(x2−0.1,x2+0.1)Uniform(x^2 - 0.1, x^2 + 0.1) distribution.

The value of correlation(X,Y)correlation(X, Y) is __________. (Answer in integer)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 0 (official GATE 2026 final answer key)

Concept used: Correlation measures only linear dependence; Cov(X,Y)=E[XY]−E[X]E[Y]Cov(X, Y) = E[XY] - E[X]E[Y].

First step: E[Y∣X]=X2E[Y \mid X] = X^2, so E[XY]=E[X3]=0E[XY] = E[X^3] = 0 by symmetry, and E[X]=0E[X] = 0.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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