how to generate a uniform random variable in the interval [-1 1] with mean zero?

Dear sir/madam,

I am working random variables. I need to know how can I generate a uniform random variable in the interval [-1 1], and also with mean zero? The function rand() generates a uniform random variable in the interval [0 1]. Looking forward to hearing from you soon.

Thanking you, BSD

Answer 1

[Javier]

You could use this code:

a=-1;b=1;
r = a + (b-a).*rand(100,1);
v=[-1:0.02:1];
v(:,v==0)=[];
plot(v,r)

Use help rand for more information!

[bsd]

Thanks for the reply. But when I checked its mean using mean(r) it is not zero.

[Walter Roberson]

There is no reason that I can see for the line

v(:,v==0)=[];

but other than that, the code

a=-1;b=1;

r = a + (b-a).*rand(100,1);

should be fine.

The mean is not zero because you are creating a random distribution, and in random distributions the mean is statistical rather than exact.

[Javier]

I use that line to plot the values among -1 and 1,to get the same number of points in x axes and y axe.

[Walter Roberson]

If you were going to do that, then I would suggest using

v=[-1:0.02:1];

first, and then using

r = a + (b-a).*rand(length(v),1);

However, I don't think plot(v,r) gives anything useful: there is no reason I can see to use [-1,1] as your X axes. You are, after all, not creating a PDF or CDF.

Answer 2

[Walter Roberson]

If you require the mean of a finite random sample of a symmetric uniform distribution to be exactly 0, then the value of the final sample is completely determined by the sum of the other samples -- the final sample would have to be exactly the negative of the rest of the sum so that the overall sum is 0. And that implies that the last sample cannot itself be random: its value is predictable by knowing the other values. You thus cannot construct a finite random sampling with an exactly fixed mean if all values are to be random.

[Oleg Komarov]

@bsd: you randomly draw from a given distribution and you get a sample.