GATE 2026 ST – Question 22

Joint Distributions · Joint and Conditional Distributions · 1 mark · Multiple choice

Let iid continuous pairs (X_i,Y_i) have joint CDF F_(X,Y)(x,y)=F_X(x)F_Y(y). For distinct sample pairs i,j find P[(X_i−X_j)(Y_i−Y_j)>0].

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Correct answer: (B) 1/2

Explanation

The coordinate differences are independent because the X and Y samples are independent. Each continuous iid difference is positive or negative with probability 1/2, with no ties. The product is positive when both signs agree: 1/4+1/4=**1/2, B**.

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