GATE 2017 CS – Question 29
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma^2$. Let $Y = \max(X, 0)$ where $\max(a, b)$ is the maximum of $a$ and $b$. The median of $Y$ is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0
Explanation
The variable $X$ is symmetric about 0, so $P(X \leq 0) = 0.5$. Whenever $X \leq 0$, $Y = 0$, so $P(Y = 0) = 0.5$. The median is the value where the cumulative probability first reaches 0.5, which is 0.