我刚刚开始使用 Octave 并试图模拟二项式随机变量的 10,000 个结果，定义为：
X ~ Bi(5, 0.2)
我用以下函数绘制了结果：
function x = generate_binomial_bernoulli(n,p,m)
% generate Bi(n, p) outcomes m times
x = zeros(1,m); % allocate array for m simulations
for i = 1:m % iterate over m simulations
successes = 0; % count the number of successful trials per simualtion (0-5)
for j = 1:n % iterate through the n trials
u = rand; % generate random nuumber from 0-1
if (u <= p) % if random number is <= p
successes++; % count it as a success
endif
end
x(i) = successes; % store the number of successful trials in this simulation
end
alphabet_x=[0:n]; % create an array from 0 to n
hist(x,alphabet_x); % plot graph
end
然后我用generate_binomial_bernoulli(5, 0.2, 10000).
这是模拟 5 次伯努利试验，每个试验的成功概率为 0.2，重复 5 次试验 10,000 次，并绘制成功次数分布图。该图显示了模拟的经验结果。
我现在还被要求绘制理论结果，我最好的猜测是在 x 轴（0.2 * 5 = 1）上围绕 1 个成功的正态分布图。
- 我怎样才能创建这个图，并将其显示在同一个直方图上？
- 我怎样才能正确地显示我的图表，其中 x 轴仅从 0 到 5，两个轴都标有标签，两个直方图用图例进行颜色编码？
编辑
这是我当前尝试绘制归一化/理论曲线的函数：
function x = generate_binomial_bernoulli(n,p,m)
% generate Bi(n, p) outcomes m times
emperical = zeros(1,m); % allocate array for m simulations
for i = 1:m % iterate over m simulations
successes = 0; % count the number of successful trials per simualtion (0-5)
for j = 1:n % iterate through the n trials
u = rand; % generate random nuumber from 0-1
if (u <= p) % if random number is <= p
successes++; % count it as a success
endif
end
emperical(i) = successes; % store the number of successful trials in this simulation
end
close all; % close any existing graphs
x_values = [0:n]; % array of x-axis values
hist(emperical, x_values, "facecolor", "r"); % plot empirical data
xlim([-0.5 (n + 0.5)]); % set x-axis to allow for histogram bar widths
hold on; % hold current graph
mean = n * p; % theoretical mean
norm = normpdf(x_values, mean, 1); % normalised y values
plot(x_values, norm, "color", "b"); % plot theoretical distribution
legend('Emprical', 'Theoretical');
end
如下图，这条曲线只沿着y轴延伸到一个非常低的高度，但我不知道如何跨越整个数据集。
