Generate random samples .

Consider two density functions

Generate random samples from a new density function for some constants and with .

[Rik]

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

[MD]

Now I even made the question clearer. The original question was missing some conditions.

Answer 1

[James Tursa]

r = rand(1,500);

Use the r values as an indicator of which distribution f or g to draw from. For those r < 0.4, generate normal random numbers from f, and generate the rest from g.

And since both f and g are normal with the same sigma of 1 but differing only in mu of 1, you could just do this (the rand( ) part simply adds a mu of 1 to those numbers to be drawn from f):

result = randn(1,500) + (rand(1,500) < 0.4);

In general, if you had two normal density functions f and g, and they had sigmas sf and sg and mus mf and mg, and you wanted to combine them with factors pf and pg (pf + pg = 1) and generate n random numbers, it would look something like this:

r = rand(1,n) < pf;
result = randn(1,n);
result(r) = result(r)*sf + mf;
result(~r) = result(~r)*sg + mg;

Or maybe someone out there knows of a function in the Statistics Toolbox that can do this.

[James Tursa]

sf = just standard deviation, not sigma^2