plt.figure(figsize=(20, 15))
x = np.linspace(0, 10, 1000)
sigma_list = [0.1, 1, 5, 10]

for sigma in sigma_list:
    my_prob = lambda x: np.exp(-x**2 / (2*sigma**2))
    plt.plot(x, my_prob(x))
plt.gca().legend(('$\sigma$ = 0.1','$\sigma$ = 1', '$\sigma$ = 5', '$\sigma$ = 10'),
                 fontsize = 20)
plt.title("High-Dimensional Probability of Pairwise Euclidean Distances", fontsize = 20)
plt.xlabel("X", fontsize = 20); plt.ylabel("P(X)", fontsize = 20)
plt.show()