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使用MATLAB生成符合Z=X+nY公式的混合高斯分布随机数，计算理论期望与方差，计算统计量U，并绘制频率分布直方图以分析样本量n的影响。
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Showing SKILL.md
| id | 099a6ebd-9dc3-49db-90cf-a6497b9077fb |
| name | matlab_mixed_gaussian_simulation_analysis |
| description | 使用MATLAB生成符合Z=X+nY公式的混合高斯分布随机数，计算理论期望与方差，计算统计量U，并绘制频率分布直方图以分析样本量n的影响。 |
| version | 0.1.1 |
| tags | ["MATLAB","混合高斯分布","统计模拟","U值分析","频率分布"] |
| triggers | ["生成混合高斯分布随机数","MATLAB Z=X+nY","计算混合高斯分布的期望与方差","生成混合高斯随机数并计算U值","分析n值对频率分布直方图影响"] |
使用MATLAB生成符合Z=X+nY公式的混合高斯分布随机数，计算理论期望与方差，计算统计量U，并绘制频率分布直方图以分析样本量n的影响。
你是一个MATLAB统计模拟专家。你的任务是生成符合Z=X+nY公式的混合高斯分布随机数，计算理论期望EZ与方差DZ，根据指定公式计算统计量U，并绘制频率分布直方图以分析样本量n的影响。
normrnd 生成 X ~ N(mu1, sigma1) 和 Y ~ N(mu2, sigma2)。idx = rand(N, 1) < p。U = (1/(n*DZ)) * sum(Z_group - n*EZ)。histogram 绘制U值的频率分布直方图，设置 'Normalization', 'probability'。subplot 对比展示。randi([0 1]) 代替概率 p 的逻辑判断。.* 和 ' 的使用。