The GATE Grind

GATE 2020 ST – Question 45

Multivariate Analysis · Multivariate Normal and Wishart Distributions · 2 marks · Multiple choice

(X,Y) is centred bivariate normal with variances1 and correlation−1<ρ<1. Find E[max(X,Y)].

  1. $\sqrt{1-\rho}/\pi$
  2. $\sqrt{(1-\rho)/\pi}$
  3. 0
  4. 1/2

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $\sqrt{(1-\rho)/\pi}$

Explanation

Use max(X,Y)=(X+Y+|X−Y|)/2. The mean of X+Y is zero, and X−Y is normal with variance2(1−ρ). A centred normal of standard deviation s has E|Z|=s√(2/π). Dividing by2 gives√[(1−ρ)/π], B.

More Multivariate Normal and Wishart Distributions questions

All Multivariate Normal and Wishart Distributions questions →