Final answer:
In linear classifiers, f(x) will be closer to the threshold when x is near the boundary. The F distribution is used in statistics to compare variances with the F statistic indicating the likelihood of group mean differences. The 90th percentile represents a critical value that delineates the top 10% of data.
Step-by-step explanation:
In the context of linear classifiers, a function f(x) provides a way to score or rank different values of x. When x is close to the boundary, the value of f(x) will be closer to the threshold that separates different classifications. This is relevant in many statistical concepts, such as the cumulative distribution function (CDF), critical values in hypothesis testing, and the F distribution used in ANOVA (Analysis of Variance).
The F distribution is particularly relevant, described by an F statistic that is always greater or equal to zero. This F statistic is calculated as the ratio between the variance among group means and the variance within the groups. A small F statistic suggests that the null hypothesis (no difference between group means) may be valid, while a large F statistic implies significant differences between the groups' means.
Finally, when discussing percentiles, like the 90th percentile, we are essentially looking at cutoff values (or critical values) that separate a certain percentage of the data. For instance, 90% of the data will fall below the 90th percentile value.