```{code-cell} python3

beta_dist = beta(2, 2)

def gen_x_draws(k):

def gen_x_draws(k, rng):

"""

Returns a flat array containing k independent draws from the

distribution of X, the underlying random variable. This distribution

bdraws[1, :] += 0.6

bdraws[2, :] -= 1.1

# Set X[i] = bdraws[j, i], where j is a random draw from {0, 1, 2}

js = np.random.randint(0, 2, size=k)

js = rng.integers(0, 2, size=k)

X = bdraws[js, np.arange(k)]

# Rescale, so that the random variable is zero mean

m, sigma = X.mean(), X.std()

nmax = 5

reps = 100000

ns = list(range(1, nmax + 1))

rng = np.random.default_rng()

# Form a matrix Z such that each column is reps independent draws of X

Z = np.empty((reps, nmax))

for i in range(nmax):

Z[:, i] = gen_x_draws(reps)

Z[:, i] = gen_x_draws(reps, rng)

# Take cumulative sum across columns

S = Z.cumsum(axis=1)

# Multiply j-th column by sqrt j