GATE 2026 DA – Question 63
Let $X$ be a random variable that follows $Uniform(-1, 1)$ distribution. The conditional distribution of the random variable $Y$ given $X = x$ is the $Uniform(x^2 - 0.1, x^2 + 0.1)$ distribution.
The value of $correlation(X, Y)$ is __________ . (*Answer in integer*)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0
Explanation
Given $X = x$, $Y$ has mean $x^2$, so $E[Y \mid X] = X^2$ and $E[XY] = E[X \cdot E[Y \mid X]] = E[X^3] = 0$, because $X$ is symmetric about 0. Also $E[X] = 0$, so the covariance is $E[XY] - E[X]E[Y] = 0$ and the correlation is 0, even though $Y$ depends strongly on $X$.