A value of 0 in Pearson's Correlation Coefficient means there's no linear correlation between the two variables. However, it's important to note that this doesn't necessarily mean there is no relationship at all, it could be that the relationship is nonlinear.

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. For a random variable, the probability distribution is the probability that the variable takes a particular value.

Spearman's correlation is a non-parametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function. This makes it suitable for both continuous and discrete ordinal variables.

You would use the Kruskal-Wallis Test when the assumptions of ANOVA (like normality or equal variances) are violated.

In a two-way ANOVA, interaction effects show how the levels of one independent variable affect the effect of the other variable on the dependent variable. Essentially, it shows whether the effect of one independent variable depends on the level of the other independent variable.

The Poisson distribution is used for describing the distribution of rare events in a large population or time/space interval. It also describes events that are independent, meaning the occurrence of one event doesn't affect the occurrence of another.

In a positively skewed distribution, the mean is usually greater than the median. A positive skew means the right tail of the distribution is longer or fatter. The mean, being affected by the values of the data points, gets dragged in the direction of the tail, and hence is typically greater than the median in a positively skewed distribution.

A normal distribution, also known as Gaussian distribution, is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean, mode and median are all equal and are located at the center of the distribution.

Nominal data is data that can be divided into categories but has no order or priority. It is a type of categorical data that simply allows us to classify or categorize. Examples include types of cuisine (Italian, Chinese, Mexican, etc.), hair color, or city of residence.

When two events are mutually exclusive, it means they cannot occur at the same time. Therefore, the probability that both will occur is 0.