The Multiplication Rule is used when we want to find the probability of two events happening at the same time. Specifically, it states that the probability of two independent events both occurring is the product of their individual probabilities.

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values. Negative skewness indicates a distribution with an asymmetric tail extending towards more negative values.

Yes, a symmetrical distribution can have nonzero kurtosis. Kurtosis is a measure of the weight in the tails, or the extreme values, which can occur in both directions, thus not affecting the symmetry. For example, a normal distribution is symmetric and has a kurtosis greater than zero.

Spearman's rank correlation coefficient is a non-parametric measure of correlation, meaning it can be used when the data is not normally distributed. It is also less sensitive to outliers compared to Pearson's coefficient. Further, it can be used to measure monotonic relationships, whether they are linear or not.

The Mann-Whitney U test is a common non-parametric statistical method used to compare two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.

A non-significant result in the Chi-square test for goodness of fit indicates that the observed distribution does not significantly differ from the expected distribution. In other words, we do not have enough evidence to reject the null hypothesis.

The Chi-square test for goodness of fit is used to test whether the observed data fits a specific distribution. It compares the observed data with the values that would be expected under the theoretical distribution.

The silhouette score is a measure of how close each point in one cluster is to the points in the neighboring clusters. It ranges from -1 (incorrect clustering) to +1 (highly dense clustering). 0 indicates overlapping clusters.

Non-parametric tests can be used with nominal, ordinal, interval, and ratio scales of measurement. This is one of the reasons why non-parametric tests are sometimes chosen over parametric ones, as they can handle data that are not interval or ratio (which are required for many parametric tests).

Homoscedasticity refers to the assumption in regression analysis that the variance of the residuals (or "errors") is constant across all levels of the independent variables.