Matlab: what is the distribution equal to in Matlab code

[Firben]

Homework Statement

A common way of displaying the distribution of a random variable is by a histogram. Consider the interval [a,b) divided into M sub-intervals (bins) of length ΔX. Given a set of N random values of x, call N_j the number of values that fall within the jth interval.

Homework Equations

If the expected value of N_j is

<N_j> = N Int(from a+(j-1)Δx to a+jΔx) P_x(x) dx ~ NΔx/2[P_x(a+(j-1)Δx) + P_x(a+jΔx)]

where ΔX = (b-a)/M

where P_x(x) is the distribution for x

The Attempt at a Solution

If i want to write a line of code that is the number of particles in a histogram bin of width Δv.

Then what is the P_x in Matlab code ? What is it equal to ? If i put P_x equal to a arbitrary number say rand(N) then is the line below then correct ?

Nj = (N.*deltaX)./2*rand(1,N); % Number of particles in a histogram of width Δv

 

[KataKoniK]

In Matlab, Px(x) represents the distribution function for the random variable x. This means that Px(x) is a function that takes in a value of x and returns the probability of that value occurring in the distribution. It cannot be set equal to a random number like rand(N). Instead, you would need to define a specific distribution function for your data and use that in your equation for <Nj>. For example, if your data follows a normal distribution, you could use the normpdf() function in Matlab to define Px(x).