Normalizing a histogram in matlab

Question

I have a histogram

hist(A, 801)

that currently resembles a normal curve but with max value at y = 1500, and mean at x = 0.5. I want to normalize it, so I tried

h = hist(A, 801)
h = h ./ sum(h)
bar(h)

now I get a normal curve with max at y = .03, but a mean at x = 450.

how do I decrease the frequency so the sum is 1, while retaining the same x range?

A is derived from

A = walk(50000, 800, .05, 2, .25, 0)

where

function [X_new] = walk(N_sim, N, mu, T, sigma, X_init)

delt = T/N;
up = sigma*sqrt(delt);
down = -sigma*sqrt(delt);

p = 1./2.*(1.+mu/sigma*sqrt(delt));

X_new = zeros(N_sim,1);
X_new(1:N_sim,1) = X_init;

ptest = zeros(N_sim,1);

for i = 1:N

    ptest(:,1) = rand(N_sim,1);
    ptest(:,1) = (ptest(:,1) <= p);

    X_new(:,1) = X_new(:,1) + ptest(:,1)*up + (1.-ptest(:,1))*down;

end

Answer 1

The sum is 1 with your code as it stands.

You may want integral equal to 1 (so that you can compare with the theoretical pdf). In that case:

[h, c] = hist(A, 801); %// c contains bin centers. They are equally spaced
h = h / sum(h) / (c(2)-c(1)); %// normalize to area 1
trapz(c,h) %// compute integral. Should be approximately 1