Let X be a standard normal random variable, and suppose Y is a contaminated normal with probability density function given by Eq. (1.1). Let Q = ρX + 1−ρ2Y , −1 ≤

ρ ≤ 1. Verify that the correlation between X and Q is

Examine how the correlation changes as K gets large with = 0.1. What does this illustrate about the robustness of ρ?

p + (1 p)(1 + K)