GATE | GATE-CS-2017 (Set 1) | Question 11

Let X be a Gaussian random variable with mean 0 and variance σ². Let Y = max(X,0) where max(a,b) is the maximum of a and b. The median of Y is _____.

Note: This questions appeared as Numerical Answer Type.
(A) 0
(B) 1
(C) 2
(D) 3


Answer: (A)

Explanation: Here, half of the values of Y are to the left of the mean X = 0 and the remaining half of the values of Y lies to the right of the mean X = 0. hence,The median of Y = 0.

Another approach :

We have for X a continuous random variable with median 0, that means :

• P(X ≤ 0) = 1/2
• P(X > 0) = 1/2

so, since X ≤ 0 → Y = 0 and X > 0 → Y > 0,

• P(Y = 0) = 1/2
• P(Y > 0) = 1/2

And definition of a median (m) of random variable Y is :

• P(Y ≤ m) ≥ 1/2
• P(Y ≥ m) ≥ 1/2

Therefore, median (m) of random variable Y is 0.

This explanation is contributed by Sumouli Chaudhary.

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