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

p 1−ρ

2Y , −1 ≤ ρ ≤ 1. Verify that the correlation between X and Q is

ρ

p

ρ

2 +(1−ρ

2

)(1− +K2

)

.

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