Question

descriptively detail how methods and applications of discrete random variables and continuous random variables are used to support areas of industry research, academic research, and scientific research.

Answer 1

Random variable is important to understand the ideas behind the various techniques, in order to know how and when to use them. One has to understand the simpler methods first, in order to grasp the more sophisticated ones. It is important to accurately assess the performance of a method, to know how well or how badly it is working. Additionally, this is an exciting research area, having important applications in science, industry, and finance. Ultimately, statistical learning is a fundamental ingredient in the training of a modern data scientist. Examples of Statistical Learning problems include:

• Identify the risk factors for prostate cancer.
• Predict whether someone will have a heart attack on the basis of demographic, diet and clinical measurements.
• Customize an email spam detection system.
• Identify the numbers in a handwritten zip code.
• Classify a tissue sample into one of several cancer classes.
• Establish the relationship between salary and demographic variables in population survey data.
• Machine learning arose as a subfield of Artificial Intelligence.
• Statistical learning arose as a subfield of Statistics.
• Machine learning has a greater emphasis on large scale applications and prediction accuracy.
• Statistical learning emphasizes models and their interpretability, and precision and uncertainty.
• But the distinction has become and more blurred, and there is a great deal of “cross-fertilization.
• Dimension reduction reduces the problem of estimating p + 1 coefficients to the simple problem of M + 1coefficients, where M < p. This is attained by computing M different linear combinations, or projections, of the variables. Then these M projections are used as predictors to fit a linear regression model by least squares. 2 approaches for this task are principal component regression and partial least squares.