If events A and B are independent, the probability of both events occurring (P(A ∩ B)) is the product of their individual probabilities (P(A) * P(B)). This is a direct result of the Multiplication Rule for independent events.

In a Chi-square test for goodness of fit, the degrees of freedom are calculated as the number of categories minus 1.

Inference in multiple linear regression primarily involves interpreting the coefficients of the model, which represent the expected change in the response variable for each one-unit change in the respective explanatory variable, assuming all other variables are held constant.

Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values.

The variance is the square of the standard deviation. Standard deviation is a measure of dispersion in a dataset and variance is a square of it, meaning that they both represent the same concept of dispersion, but in different units.

When computing the Pearson correlation coefficient, it is assumed that there is a linear relationship between the variables. Furthermore, it's also assumed that the variables are continuous and that the data is homoscedastic (i.e., the variance of the errors is the same across all levels of the variables).

Conditional independence of A and B given C means that knowing that C has occurred does not change the relationship between A and B. In other words, the occurrence of event C does not affect the independence of events A and B.

Normalization or standardization ensures that all features contribute equally to the final distance calculation, regardless of their original scale. Without this step, features with larger scales would dominate the distance calculation, potentially leading to misleading clusters.

The height of a bar in a histogram represents the frequency (or relative frequency) of data for that particular bin. This means the taller the bar, the more data falls into that specific interval.

The power of a test is influenced by the effect size - the magnitude of the difference or relationship you're testing for. Larger effect sizes increase the power of a test because they create a larger signal relative to the noise, making it easier to detect an effect if one exists.

The Central Limit Theorem (CLT) is often used in scenarios where we are interested in the average outcome of a large number of independent or nearly independent events. This is commonly the case when we are making inferences about a population based on a sample.

The Central Limit Theorem states that, with a large enough sample size, the distribution of the sample mean will be approximately normally distributed. This allows us to use Z-tests even when the population is not normally distributed.