Principal components share independence but not a common variance

Let $\underline X\sim N_4(\underline\mu,\Sigma)$ where eigen values of $\Sigma$ are given by $\lambda_1=6,\lambda_2=4,\lambda_3=3, \lambda_4=2$. Let $Y_i$ be the principal component corresponding to $\lambda_i, i=1,2,3,4$. Then which of the following statements is not correct?