Logistic Regression - malty classification

Question

I want to understand why the probability of P(D|p) is presented as a product of mentioned probabilities. I read a lot of texts, but everywhere the explanations are full of terminologies to confuse the reader.

Thanks!!!

Answer 1

Let $Y_i$ be random variable that shows the value of data in the $i$th experiment. Because of the assumption that data is gathered from independent and identically distributed (with distribution $p$) experiments, $Y_i$s are IID random variables. Therefore you have:

$$ \begin{align} P(D\mid p) &= P(Y_1=y_1, Y_2 = y_2, \dots ,Y_n = y_n \mid p) \\ &= P(Y_1 = y_1\mid p)P(Y_1 = y_1\mid p)\dots P(Y_n = y_1\mid p) \end{align} $$