The normal distribution is also known as the Gaussian distribution. It is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is bell-shaped.

The probability of the intersection of two independent events is calculated as the product of their individual probabilities. So if A and B are independent, P(A ∩ B) = P(A) * P(B). This is a direct result of the Multiplication Rule for independent events.

Qualitative data represents characteristics or attributes. It is often non-numerical and may include qualities such as textures, colors, smells, tastes, appearance, beauty, etc. This data type is commonly used in fields such as sociology, marketing, and psychology.

The strength of correlation between two variables is determined by the correlation coefficient. A value close to +1 or -1 indicates a strong correlation, while a value close to 0 indicates a weak or no correlation.

Larger sample sizes increase the power of the Kruskal-Wallis Test. Power is the ability of a test to detect a true effect when there is one.

Polynomial regression allows us to model the relationship between the dependent variable and independent variables as a non-linear equation. This is achieved by raising independent variables to a power, allowing the model to fit more complex data patterns.

The median is usually the most reliable measure of central tendency when a data distribution is skewed. Unlike the mean, the median isn't influenced by extreme values. Therefore, in a skewed distribution, the median generally gives a better idea of the typical value than the mean.

A dendrogram is a tree-like diagram that is used in hierarchical clustering to represent the hierarchy of clusters. Each join in the dendrogram represents the two clusters merging, and the height of the join is the distance between those clusters.

The residuals vs fitted values plot is commonly used in regression diagnostics to check the assumptions of linearity and equal variance (homoscedasticity). The residuals should be scattered randomly around zero, and the spread of the residuals should not change with the fitted values.

A random variable is a variable whose possible values are outcomes of a random event. It can be either discrete (having specific values) or continuous (any value within a certain range).

Quantitative data can be classified into two subtypes: discrete and continuous. Discrete data can only take certain values (like the number of children in a family – 1, 2, 3, etc.) and Continuous data can take any value within a given range or continuum (like height or weight of a person).

A probability mass function is used for discrete random variables and gives the probability that a discrete random variable is exactly equal to some value. A probability density function, on the other hand, is used for continuous random variables and gives the density of the variable at a particular value.