practice – Problem 1
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import numpy as np
from scipy.stats import uniform
## record your uni here
Problem 1 (25 points)¶
Let $$\theta = \int_0^1 \int_0^y \exp(-x^2) x^4 dx dy$$
Use the monte carlo method to estimate $\theta$.
np.random.seed(42)
n = 10_000
U = uniform.rvs(size=(n,2))
f = np.exp(-U[:,0]**2) * (U[:,0] ** 4)
loc = U[:,0] > U[:,1]
f[loc] = 0
theta = np.mean(f)
print(theta)
0.008551462974661273
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