How do I estimation of the means of a random variable?

Question

Zaref Li 2021-11-9

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582874-how-do-i-estimation-of-the-means-of-a-random-variable

回答： Sulaymon Eshkabilov 2021-11-9

Hi everyone. I'm trying to understand this code. Are these operations done for the Gaussian random variable? How do I change the Gaussain random variable? Should I write normrnd() instead of rand()?

% lower and upper bounds of the Uniform random variable X:
a= 0;
b = 2;
% True values of the mean and variance of X:
m = (b-a) / 2;
v = (b-a)^2 / 12;
N = 10; % Number of observations
m_h = zeros(1,N); % Preallocation for speed
% Estimation of the mean and variance:
for i = 1 :10
    X = b * rand(N,1);
    m_h(i) = sum (X) / N;
    
end
v_h = v/N;
% Mean value of the estimates:
m_h_mean = sum (m_h,2)/N;
% Demonstrate the results:
disp([ 'Mean value of the estimates is: ',num2str(m_h_mean)])
disp([' True mean value of X is: ',num2str(m)])
stem(m_h)
hold
M = m*ones(1,length(m_h)+2);
plot(0:11,M)
M_h = m_h_mean*ones(1,length(m_h)+2);
plot(0:11,M_h, ' --')
axis([0 10.5 0 2])

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Star Strider 2021-11-9

The rand function creates uniformly-distribured random numbers on the interval [0,1] while randn creates normally distributed random numbers

, so multiplying it changes σ and adding to it changes μ.

Choose the function that returns the desired result.

.

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Answer 1

Sulaymon Eshkabilov 2021-11-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582874-how-do-i-estimation-of-the-means-of-a-random-variable#answer_827864

在 MATLAB Online 中打开

% lower and upper bounds of the Uniform random variable X:
a= 0;
b = 2;
% True values of the mean and variance of X:
m = (b-a) / 2;
v = (b-a)^2 / 12;
N = 10; % Number of observations
m_h = zeros(1,N); % Preallocation for speed
mu0=30;                  % Single Mean value of population 
% mu0=[30:20:100];       % A few different mean values of population 
sigma0=3.5;                % STD 
SETs = 1;                  % How many sets of Population to generate
% SETs = 5;                % Five sets of Population to generate in each
% iteration
% Estimation of the mean and variance:
for i = 1 :10
X = normrnd(mu0, sigma0, N, SETs);
m_h(i) = mean(X); 
end
% OR without [for .. end] loop, use this one:
X2 = normrnd(mu0, sigma0, N, N);
m_h2 = mean(X2,2); 
...