To understand the formula above, we need to comprehend the random variables $${\displaystyle \operatorname {E} [Y|X]}$$ and See more

Example 1
Five graduate students take an exam that is graded from 0 to 100. Let $${\displaystyle Y}$$ denote the student's grade and See more

A similar law for the third central moment $${\displaystyle \mu _{3}}$$ says
For higher cumulants, a generalization exists. See law of total cumulance. See more

Finite Case
Let $${\displaystyle (x_{1},y_{1}),\ldots ,(x_{n},y_{n})}$$ be observed values of $${\displaystyle (X,Y)}$$, with repetitions.
Set $${\displaystyle {\bar {y}}=\operatorname {E} [Y]}$$ and, for each possible value See more

• Law of total covariance – Formula in probability theory − a generalization
• Law of propagation of errors – Effect of variables' … See more