### Random Variables and Distributions

Recall that `numpy.random` provides functions for generating random variables

Recall that `numpy.random` provides tools for generating random variables

```{code-cell} python3

np.random.beta(5, 5, size=3)

rng = np.random.default_rng()

rng.beta(5, 5, size=3)

```

This generates a draw from the distribution with the density function below when `a, b = 5, 5`

```{code-cell} python3

from scipy.stats import linregress

x = np.random.randn(200)

y = 2 * x + 0.1 * np.random.randn(200)

x = rng.standard_normal(200)

y = 2 * x + 0.1 * rng.standard_normal(200)

gradient, intercept, r_value, p_value, std_err = linregress(x, y)

gradient, intercept

```

Here is one solution:

```{code-cell} ipython3

rng = np.random.default_rng()

M = 10_000_000

S = np.exp(μ + σ * np.random.randn(M))

S = np.exp(μ + σ * rng.standard_normal(M))

return_draws = np.maximum(S - K, 0)

P = β**n * np.mean(return_draws)

print(f"The Monte Carlo option price is {P:3f}")