Excel is a spreadsheet software, while R, SAS, and MATLAB are statistical software packages specifically designed for statistical analysis and data manipulation.

A probability distribution is used to model the behavior of random variables, calculate the expected value and variance of a random variable, and make inferences about the population from which the data was drawn.

A sample is a subset of the population selected to represent the entire population. The population is the entire group of individuals or objects from which the sample is drawn.

A pseudo-random number generator is a computer algorithm that generates a sequence of numbers that appear to be random, but are actually determined by a deterministic process.

A hypothesis test is used to determine if there is a statistically significant difference between two groups or populations.

A Type I error is rejecting a true null hypothesis, while a Type II error is accepting a false null hypothesis. A Type I error is more serious than a Type II error because it leads to a false positive conclusion, while a Type II error leads to a false negative conclusion.

Scatter plots, histograms, bar charts, and pie charts are all common methods for visualizing data in statistical computing.

Regression analysis is used to model the relationship between two or more variables, predict the value of one variable based on the values of other variables, and determine the correlation between two variables.

K-means clustering, hierarchical clustering, and density-based clustering are all common methods for clustering data in statistical computing.

Time series analysis is used to analyze data that is collected over time, identify trends and patterns in time series data, and forecast future values of a time series.

Bootstrapping, jackknifing, and cross-validation are all common methods for resampling data in statistical computing.

Meta-analysis is used to combine the results of multiple studies to increase the overall sample size and reduce the bias of the individual studies.

Imputation, deletion, and weighting are all common methods for dealing with missing data in statistical computing.

A statistical model is used to represent the relationship between variables, make predictions about future events, and test hypotheses.

Mean squared error, root mean squared error, Akaike information criterion, and Bayesian information criterion are all common methods for evaluating the performance of a statistical model.