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.
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.
Quiz of this Question