The GATE Grind

GATE 2022 ST – Question 41

Joint Distributions · Joint and Conditional Distributions · 2 marks · Multiple choice

The joint density of (X,Y,Z) is (2x+3y+z)/3 on the unit cube,zero elsewhere. Which point lies on the regression surface of X on (Y,Z)?

  1. (4/7,1/3,1/3)
  2. (6/7,2/3,2/3)
  3. (1/2,1/3,2/3)
  4. (1/2,2/3,1/3)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) (4/7,1/3,1/3)

Explanation

Integrate over x:the conditional denominator is 1+3y+z. The conditional first-moment numerator is 2/3+(3y+z)/2. At y=z=1/3,this ratio is (2/3+2/3)/(1+4/3)=4/7. For all finite y,z in the cube,the ratio exceeds 1/2,excluding C,D,and B’s value is too large. **A**.

More Joint and Conditional Distributions questions

All Joint and Conditional Distributions questions →