fix issues with mix_model

Author: mmcky

lectures/mix_model.md

@@ -455,7 +455,7 @@ def plot_π_seq(α, π1=0.2, π2=0.8, T=200):
     # plot
     fig, ax1 = plt.subplots()
     for i in range(2):
-        ax1.plot(range(T+1), π_seq_mixed[i, :], label=fr"$\pi_0$={π_seq_mixed[i, 0]}")
+        ax1.plot(range(T+1), π_seq_mixed[i, :], label=rf"$\pi_0$={π_seq_mixed[i, 0]}")
 
     ax1.plot(np.nan, np.nan,  '--', color='b', label='Log likelihood ratio process')
     ax1.set_ylabel("$\pi_t$")
@@ -720,7 +720,7 @@ for i in range(len(sizes)):
     )
 ax.set_title(r'$\pi_t(\\alpha)$ as $t$ increases')
 ax.legend()
-ax.set_xlabel(r'$\\alpha$')
+ax.set_xlabel('$\\alpha$')
 plt.show()
 ```