Shrinkage intensity in closed form

Let $x_t \sim N(0, I_n)$ i.i.d., $t = 1..T$, mean known, and $S = \frac1T\sum_t x_tx_t^\top$. (a) Show $\mathbb E\|S - I\|_F^2 = n(n+1)/T$ (unnormalised Frobenius norm). (b) For the (deliberately wrong) target $F = \tfrac12I$, compute $\delta^*$ from (14.4) and evaluate it for $n = 30$, $T = 60$. (c) Show $\delta^* \in [0, 1]$ in general and interpret the limits $T \to \infty$ and $F = \Sigma$.