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The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
Pygmalion in the Classroom is a 1968 book by Robert Rosenthal and Lenore Jacobson about the effects of teacher expectation on first and second grade student performance. [1] The idea conveyed in the book is that if teachers' expectations about student ability are manipulated early, those expectations will carry over to affect teacher behavior ...
A 2005 meta-analysis of 35 years of research on teacher expectations found that, while self-fulfilling prophecies in the classroom do occur, the effects are usually small and temporary. It is unknown whether self-fulfilling prophecies affect intelligence or have an otherwise harmful effect.
In probability theory, the law of total variance [1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and are random variables on the same probability space, and the variance of is finite, then
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...
The law of iterated logarithms operates "in between" the law of large numbers and the central limit theorem. There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums S n, scaled by n −1, converge to zero, respectively in probability and almost surely:
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