7. Statistiscs

数学英语



周维祺

Population vs. Sample

  • population: the subject of study

  • sample: measurements drawn from populations

  • both are realizations of some random variable(s)

Average (Mean)

  • Arithmetic mean:

  • Geometric mean:

  • Harmonic mean:

Mode

The item with highest occurence in a sequence

Median

The half way point in a sorted sequence , i.e.,

Covariance and Correlation

  • Covariance:

  • Correlation:

Estimator

A function on samples that
aims to estimate a property of the population

Criteria for Estimators

  • Consistency
    consistent if as the sample size grows

  • Bias:
    unbiased: the bias is

  • Efficiency
    efficient if the variance of the estimator is small

Confidence Interval

The interval that inscribes a given concentration of an estimator

Maximal Likelihood

The procedure of determining parameters that maximizes the probability of measurements

Hypothesis Testing

Determines the probability of whether a given hypothesis is true

Null Hypotheis: ; Alernative Hypotheis:

Corollaries and Propositions

  • Lemma: A less important, often technical intermediate statement

  • Theorem: An important result

  • Corollary: An immediate consequence of a theorem

  • Proposition: (1) A less significant statement that is not a lemma, or (2) used interchangably with corollary

Summary

  • Basic terms

  • Estimators and its criteria

  • Maximal likelihood and statistical testing

  • Corollaries and propositions