Plot the function
f(x) = sin2(x − 2)e−x2
over the interval [0, 2]. Add proper axis labels, a title, etc.
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 2, 50)
y = np.square(np.sin(x - 2)) * np.exp(-x * x)
plt.figure(num = '作图')
plt.plot(x, y)
plt.title('f(x) = sin2(x − 2)e−x2')
plt.xlabel('x')
plt.ylabel('y')
plt.show()
结果：
Exercise 11.2: Data
Create a data matrix X with 20 observations of 10 variables. Generate a vector b with parameters Then
generate the response vector y = Xb+z where z is a vector with standard normally distributed variables.
Now (by only using y and X), find an estimator for b, by solving
ˆ b = arg min
b
kXb − yk2
Plot the true parameters b and estimated parameters ˆ b. See Figure 1 for an example plot.
import matplotlib.pyplot as plt
import numpy as np
X = np.random.rand(20, 10) * 10
z = np.random.normal(0, 1, size=(20, 1))
b = np.random.rand(10, 1)
y = np.dot(X, b) + z
x = np.linspace(-1, 1, 10)
bhat = np.array(np.linalg.lstsq(X, y, rcond=-1)[0])
plt.scatter(x, b, c='r', marker='s', label="true b")
plt.scatter(x, bhat, c='g', marker='o', label='estimated b')
plt.legend()
plt.xlabel('x')
plt.show()
Exercise 11.3: Histogram and density estimation
Generate a vector z of 10000 observations from your favorite exotic distribution. Then make a plot that
shows a histogram of z (with 25 bins), along with an estimate for the density, using a Gaussian kernel
density estimator (see scipy.stats). See Figure 2 for an example plot.
import numpy as np
import matplotlib.pyplot as plt
import seaborn
z = np.random.normal(0 , 1, size=(10000))
#plt.hist(z, 25, facecolor='g', edgecolor='b',density=True)
seaborn.distplot(z, bins=25, kde=True)
plt.show()
