import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

# 生成模拟数据
data = np.random.normal(loc=75, scale=10, size=1000)

# 绘制分布图
sns.histplot(data, bins=30, kde=True)
plt.title('Student Scores Distribution')
plt.xlabel('Scores')
plt.ylabel('Frequency')
plt.show()

# 假设有以下条件：
P_A = 0.01  # 疾病的先验概率
P_B_given_A = 0.9  # 得到症状的条件概率
P_B = 0.02  # 获得症状的总体概率

# 计算后验概率
P_A_given_B = (P_B_given_A * P_A) / P_B
print(f"P(Disease | Symptom) = {P_A_given_B:.4f}")

# 骰子的可能结果和对应的概率
outcomes = np.array([1, 2, 3, 4, 5, 6])
probabilities = np.array([1/6] * 6)

# 期望值
expected_value = np.sum(outcomes * probabilities)

# 方差
variance = np.sum((outcomes - expected_value)**2 * probabilities)

print(f"Expected Value: {expected_value:.2f}")
print(f"Variance: {variance:.2f}")

import numpy as np

# 状态转移矩阵
transition_matrix = np.array([[0.8, 0.2],  # 晴天到晴天和雨天的概率
                               [0.4, 0.6]]) # 雨天到晴天和雨天的概率

# 初始状态
state = np.array([1, 0])  # 1表示晴天，0表示雨天

# 模拟10天的天气变化
for day in range(10):
    state = np.dot(state, transition_matrix)
    print(f"Day {day+1}: Sunny Probability: {state[0]:.2f}, Rainy Probability: {state[1]:.2f}")

import numpy as np

n = 1000000  # 生成的随机点的数量
inside_circle = 0

for _ in range(n):
    x, y = np.random.uniform(-1, 1, 2)  # 随机生成点
    if x**2 + y**2 <= 1:  # 判断是否在单位圆内
        inside_circle += 1

pi_estimate = 4 * inside_circle / n
print(f"Estimated π: {pi_estimate:.5f}")

import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt

# 创建数据集
data = {
    '面积': [1500, 2000, 2500, 3000],
    '房价': [300000, 400000, 500000, 600000]
}
df = pd.DataFrame(data)

# 准备训练数据
X = df[['面积']]  # 自变量
y = df['房价']    # 因变量

# 创建并训练模型
model = LinearRegression()
model.fit(X, y)

# 打印模型参数
print("截距:", model.intercept_)
print("斜率:", model.coef_[0])

# 预测
面积新房 = np.array([[2200]])
预测房价 = model.predict(面积新房)
print(f"2200平方英尺房子的预测价格为: {预测房价[0]}美金")

# 可视化
plt.scatter(X, y, color='blue', label='实际数据')
plt.plot(X, model.predict(X), color='red', label='预测线')
plt.xlabel('面积 (平方英尺)')
plt.ylabel('房价 (美金)')
plt.title('面积与房价的线性回归')
plt.legend()
plt.show()

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression

# 创建数据框
data = pd.DataFrame({
    'Age': [30, 45, 35, 50],
    'Weight': [70, 85, 75, 90],
    'Diabetes': [0, 1, 0, 1]
})

# 特征和标签
X = data[['Age', 'Weight']]
y = data['Diabetes']

# 拆分数据为训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=0)

# 创建并训练逻辑回归模型
model = LogisticRegression()
model.fit(X_train, y_train)

# 预测
predictions = model.predict(X_test)
probabilities = model.predict_proba(X_test)
print("Predictions:", predictions)
print("Probabilities:", probabilities)