# Example of statistics coursework

where ( ω B | A S , ω B | ¬ A S ) {\displaystyle (\omega _{B|A}^{S},\omega _{B|\lnot A}^{S})} denotes a pair of binomial conditional opinions, as expressed by source S {\displaystyle S} . The parameter a A {\displaystyle a_{A}} denotes the prior probability (aka. the base rate ) of A {\displaystyle A} . The pair of inverted conditional opinions is denoted ( ω A | ~ B S , ω A | ~ ¬ B S ) {\displaystyle (\omega _{A{\tilde {|}}B}^{S},\omega _{A{\tilde {|}}\lnot B}^{S})} . The conditional opinion ω A | B S {\displaystyle \omega _{A|B}^{S}} generalizes the probabilistic conditional P ( A ∣ B ) {\displaystyle P(A\mid B)} , . in addition to assigning a probability the source S {\displaystyle S} can assign any subjective opinion to the conditional statement ( A ∣ B ) {\displaystyle (A\mid B)} . A binomial subjective opinion ω A S {\displaystyle \omega _{A}^{S}} is the belief in the truth of statement A {\displaystyle A} with degrees of uncertainty, as expressed by source S {\displaystyle S} . Every subjective opinion has a corresponding projected probability P ( ω A S ) {\displaystyle P(\omega _{A}^{S})} . The projected probability of opinions applied to Bayes' theorem produces a homomorphism so that Bayes' theorem can be expressed in terms of the projected probabilities of opinions:

The χ2 (Chi-Squared) Goodness-of-Fit Test uses a measure of goodness of fit which is the sum of differences between observed and expected outcome frequencies (that is, counts of observations), each squared and divided by the number of observations expected given the hypothesized distribution. The resulting χ2 statistic, chiSquared , can be compared to the chi-squared distribution to determine the goodness of fit. In order to determine the degrees of freedom of the chi-squared distribution, one takes the total number of observed frequencies and subtracts the number of estimated parameters. The test statistic follows, approximately, a chi-square distribution with (k − c) degrees of freedom where k is the number of non-empty cells and c is the number of estimated parameters for the distribution.

With this philosophy in mind, the ESRB administers a three-part rating system that includes Rating Categories to suggest age-appropriateness, Content Descriptors to indicate what type of content may have triggered the rating and/or may be of interest or concern to the consumer, and Interactive Elements, which advise about user interactions, the sharing of users’ locations with others, if in-app purchases of digital goods are completed and/or if unrestricted internet access is provided. The result is a rating system that is widely adopted by game publishers, supported by retailers, and which is consistently described by parents and opinion leaders as the best entertainment rating system in the US.