The GATE Grind

GATE 2023 ST – Question 47

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

The joint PMF is p(x,y)=c/2^(x+y+2) for nonnegative integers x≠y,zero otherwise. Which holds?

  1. c=1/2
  2. c=1/4
  3. c>1
  4. X and Y are independent.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) c>1

Explanation

The unrestricted geometric double sum is (Σ_(x≥0)2^(−x−1))²=1. The removed diagonal sum is Σ_(x≥0)2^(−2x−2)=1/3. Normalization gives c(2/3)=1,so c=3/2>1. Independence fails because all diagonal probabilities vanish while the marginals are positive there. **C**.

More Joint and Conditional Distributions questions

All Joint and Conditional Distributions questions →