Generate Random Sample of 0's and 1's

Hi guys,

how do I generate a random sample of 0's and 1's of size N, such that the probability of of 1 being chosen is p.

I can create a permutation however I can't seem to incorporate probability p into it. Plus, also is there a way I could quickly sum the components of the permutation.

Thanks,

Joe

Answer 1

[Suneesh]

MATLAB has a function RANDSRC (part of the Comm Sys Tbx) which does this.

out = randsrc(1,N,[0 1; (1-p) p])

See documentation for the function to learn more about the usage.

[Joe]

thanks this is useful, how about summing the individual components, is there a function?

[Suneesh]

The SUM function

http://www.mathworks.com/help/matlab/ref/sum.html

Answer 2

[Rajiv Ghosh-Roy]

How about

a = rand(1, N) < p

This creates a random vector of size N, and the < will return 1 if true, 0 if false.

[Joe]

I understand how rand(1,N) generates a sequence of N random integers but isn't this based on the uniform distribution? How does introducing <p mean a 1 occurs with probability p?

[José-Luis]

It does not generate integers. It gives values from a normal random distribution with mean 0 and variance of 1. That makes Rajiv's suggestion valid.

[Rajiv Ghosh-Roy]

Please consult the help for rand. rand(1, N) will generate a 1xN vector of random numbers uniformly distributed in [0, 1]. The probability that a number is in (0, p) is then p.

[Suneesh]

Joe, your problem may be stated as "Generate random numbers that have a Bernoulli distribution with the head(1) probability = p". There are several algorithms for generating random numbers and many start with generating random numbers that are uniformly distributed. This is what RAND does. The comparison " < p" owes to the inverse transform method of generating arbitrarily distributed random numbers from a uniform distribution. However, as far as I remember it should be "<=p". This method is standard in several text books on beginning probability theory. See also:

1. http://www.mathworks.com/help/stats/common-generation-methods.html

2. "Inverse Transform Method for simulating continuous random variables." in

http://www.cs.bgu.ac.il/~mps042/invtransnote.htm