# Frequency distribution and number of samples

Suppose I have a frequency distribution of some process of f_n(x) that is based on n samples, with n < N. I want to know the frequency distribution f_N(x) for N samples. The process was in n timesteps, and what I want to do is use the same distribution for a larger number of timesteps. The timesteps for both timeseries are the same.

Is it correct to just scale f_n by a factor N/n, so that I get

f_N(x) = N/n f_n(x)

What is the reasoning behind it?

• Are the timesteps smaller (i.e. faster sampling over an equivalent time period) or are they the same (i.e same sampling rate over a longer period)? – MikeP Oct 10 '14 at 15:06
• They're the same. I updated the question. – jjack Oct 10 '14 at 15:10