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  2. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    That is, the expected value to be won from a $1 bet is −$ ⁠ 1 / 19 ⁠. Thus, in 190 bets, the net loss will probably be about $10. Thus, in 190 bets, the net loss will probably be about $10. Random variables with countably infinitely many outcomes

  3. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve). Main article: Central limit theorem The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution.

  4. Method of moments (statistics) - Wikipedia

    en.wikipedia.org/wiki/Method_of_moments_(statistics)

    In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis.. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.

  5. Bias of an estimator - Wikipedia

    en.wikipedia.org/wiki/Bias_of_an_estimator

    This can be seen by noting the following formula, which follows from the Bienaymé formula, for the term in the inequality for the expectation of the uncorrected sample variance above: ⁡ [(¯)] =. In other words, the expected value of the uncorrected sample variance does not equal the population variance σ 2 , unless multiplied by a ...

  6. Mean squared error - Wikipedia

    en.wikipedia.org/wiki/Mean_squared_error

    To minimize MSE, the model could be more accurate, which would mean the model is closer to actual data. One example of a linear regression using this method is the least squares method—which evaluates appropriateness of linear regression model to model bivariate dataset, [6] but whose limitation is related to known distribution of the data.

  7. Prior probability - Wikipedia

    en.wikipedia.org/wiki/Prior_probability

    An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature, or a distribution of the temperature for ...

  8. Estimator - Wikipedia

    en.wikipedia.org/wiki/Estimator

    In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...

  9. Prediction interval - Wikipedia

    en.wikipedia.org/wiki/Prediction_interval

    Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".