If I have a step-wise distribution of frequencies (f) for constant bins on the x-axis (x), how do I get new values of f given a new mean (X) without changing any of the bins?
In other words, if f1+f2+...+fn = 1, and the bins on the x-axis remain constant, how do I solve the right side of this equation when X is multiplied by some factor a?:
X * (a) = f1*x1 + f2*x2 + ... + fn*xn
If I multiply all the f values by a, the f's no longer sum to 1...