$15$ p$.)$ Re$-$create the automatic iterative threshold finding algorithm using the normalized histogram $($pi$)$ of the image instead of the image itself

Express $($use the expressions given below and directly calculate the averages of the two classes when the image is thresholded with a T threshold value$).$

remember how to calculate it from the normalized histogram$).$ In this algorithm, the initial threshold value is the average of the image.

Explain why it was chosen as the value.