how can I generate data mixture of 2 Normal distributions and has the form f(x) = 0.4X1 + 0.6X2 where X1 ~ N(0.4 ,0.15^2) and X2 ~ N(0.7 , 0.09^2)?

i need help to generate data from two mixture normal distributions of the denstiy function f(x)=0.4*x1+0.6*x2 where x1~N(0.4,0.15^2) & x2~N(0.7,0.09^2)

[the cyclist]

I interpreted what you wrote a little bit differently from the math you actually wrote. Did you mean that you want there to be 40% probability that the draw is from x1, and 60% that it is from x2? (That's what I assume you meant.)

Answer 1

[the cyclist]

Here is one way:

% The number of random samples to generate
N = 10000;

% First, generate a binomial variable, which 40% of the time (on average) will be equal to 1,
% and 60% of the time (on average) will be equal to zero.
frac = rand(N,1) < 0.4;

% Generate the two normal distributions to sample from
norm1 = 0.4 + 0.15*randn(N,1);
norm2 = 0.7 + 0.09*randn(N,1);

% If "frac" is equal to 1, then the choice will be from the first normal.
% If "frac" is equal to 0, then the choice will be from the second normal.
d = frac.*norm1 + (1-frac).*norm2;

% Plot the resulting distribution
figure
histogram(d)

[the cyclist]

[ali talib]

thanks alot

but, could you explain me the technik

[the cyclist]

I've commented the code to explain what is happening.

[Deepak Kumar]

what we will do, if we need to calculate (N1 / N2) distribution?

[Torsten]

What do you mean by "calculate" ?