Let X be a Gaussian random variable with mean 0 and variance 2. Let Y = (X, 0) where (a,b) is the maximum of a and b. The median of Y is …

Official answer: 0. Explanation: Since X N(0, 2) is symmetric about 0: P(X 0) = 0.5 and P(X > 0) = 0.5 Now consider the transformed random variable Y = (X, 0): - For X 0, Y = 0. - For X > 0, Y = X > 0. The cumulative distribution function (CDF) of Y, FY(y) = P(Y y), satisfies: - For y 0: FY(y) = P(X y) > 0.5 By definition, a median m of Y must satisfy P(Y m) 0.5 and P(Y m) 0.5. At m = 0: P(Y 0) = 0.5 0.5 and P(Y 0) = 1.0 0.5 Thus, the median of Y is 0.

Engineering Mathematics · Probability and Statistics

Official IIT answer key · IIT Roorkee · Audited Aug 2026

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GATE CSE 2017 Set 1 Q19 · NAT · 1 mark

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 ________.

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Probability and Statistics

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How GATE tests Probability and Statistics

Probability and Statistics in GATE CS is consistently tested with 2 to 4 questions per year, spanning fundamental combinatorics, conditional probability, Bayes' theorem, discrete and continuous random variables, and expectation/variance properties. A notable proportion of questions require setting up a discrete probability model (urn/coin/dice experiments or bit strings) or computing expectations using linearity of expectation and integration over piece-wise uniform intervals. The question mix favors NAT and conceptual MCQ/MSQ formats with an emphasis on exact algebraic reasoning rather than heavy numerical statistical testing.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Engineering Mathematics · Probability and Statistics

Official IIT answer key · IIT Roorkee · Audited Aug 2026

Take topic test

GATE CSE 2017 Set 1 Q19 · NAT · 1 mark

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 ________.

Numerical answer

Enter a value to check

Key concept

Probability and Statistics

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Probability and Statistics

Full Probability and Statistics guide →

More on Probability and Statistics

All 46 questions on Probability and Statistics →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

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 ________.

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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 ________.

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Let XXX be a Gaussian random variable with mean 000 and variance σ2\sigma^2σ2. Let Y=max⁡(X,0)Y = \max(X, 0)Y=max(X,0) where max⁡(a,b)\max(a,b)max(a,b) is the maximum of aaa and bbb. The median of YYY is ________.

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Let XXX be a Gaussian random variable with mean 000 and variance σ2\sigma^2σ2. Let Y=max⁡(X,0)Y = \max(X, 0)Y=max(X,0) where max⁡(a,b)\max(a,b)max(a,b) is the maximum of aaa and bbb. The median of YYY is ________.

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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 ________.

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 ________.