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.

The power of a statistical test is the probability that it correctly rejects a false null hypothesis. In other words, it is 1 minus the probability of making a Type II error.

The normal distribution, also known as Gaussian distribution, is a continuous probability distribution that has a bell-shaped curve. It is symmetrical around its mean, implying that the data near the mean are more frequent in occurrence than data far from the mean.

Non-parametric tests might be used over parametric ones when the data does not meet the assumptions for a parametric test, such as when the data does not follow a normal distribution, when the variances are not equal across groups, or when the data are ordinal or nominal rather than interval or ratio.

Non-parametric tests are used when the data doesn't meet the assumptions of parametric tests like the t-test, such as when the data is not normally distributed.

If the p-value in a Chi-square test is less than the chosen significance level, we reject the null hypothesis. This means that we have enough evidence to conclude that the two variables are not independent.

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.