Bayes' theorem can be applied to hypothesis testing by calculating the probability of the hypothesis given the observed data. This differs from traditional frequentist hypothesis testing, where the data is assumed given and the hypothesis is tested.

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. Positive kurtosis indicates a distribution with tails or outliers that are fatter and more extreme than a normal distribution.

Descriptive statistics summarizes and interprets the characteristics of a dataset. These characteristics can include measures of central tendency like mean, median, and mode, measures of dispersion like range, variance, and standard deviation, and measures of shape like skewness and kurtosis. This branch of statistics provides a summary about the samples and the measures that have been made. It's essentially a way to describe and summarize the data.

The range of a discrete random variable is the set of all possible outcomes or values that the variable can take.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that the sampling distribution of a mean will approach normality as the sample size increases, regardless of the shape of the population distribution. The importance of CLT is that it enables us to make statistical inferences about the population mean based on the properties of the normal distribution.

The power of a test is the probability that it correctly rejects a false null hypothesis. This is essentially the ability of the test to detect an effect or difference if it truly exists. It's the complement of the Type II error rate (beta).

For a discrete random variable, the sum of all probabilities must equal to 1. This is because it represents a complete enumeration of all possible outcomes of the random variable, which together encompass all possibilities.

Multicollinearity refers to the situation in multiple linear regression where the predictor variables are highly correlated. This can lead to unstable estimates of the coefficients which can change erratically in response to small changes in the model.

Multicollinearity can be addressed by removing one or more of the highly correlated independent variables.

Bayesian methods, which are grounded in Bayes' theorem, play an integral role in many areas of machine learning. They allow the model to update its predictions as it receives more data, making them particularly useful for tasks involving prediction and recommendation.