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A) 0

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.

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