Calculate Standard deviation from pdf

Hello,

I'm new to Matlab and trying to use it to estimate standard deviation of distribution from pdf of a distribution. I have random values and probability for these value like to following:

Values (Prob) 10 (0.1) 11 (0.2) 12 (0.4) 13 (0.05) 14 (0.05) 15 (0.2)

Is there any function/code to estimate the standard distribution? Thanks.

Answer 1

[Star Strider]

These are termed a weighted mean and standard deviation:

% % % References: 
% % % https://en.wikipedia.org/wiki/Weighted_standard_deviation#Weighted_sample_variance
% % % http://itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf
% 
% 10 (0.1) 11 (0.2) 12 (0.4) 13 (0.05) 14 (0.05) 15 (0.2)

X = 10:15;                          % Data
W = [0.1 0.2 0.4 0.05 0.05 0.2];    % Weights
N = length(X);

Wmean = X*W'/sum(W);                % Weighted mean

Wstd = sqrt((sum(W.*(X - Wmean).^2)/N) / ((N-1)*sum(W)/N)); % Weighted std

[zorra2578]

Thank you very much.

[Star Strider]

My pleasure!

[Xiao Yang]

I don't think the first "/N" should be there in the calculation of Wstd