Valencia College Joint Probability Distributions and Random Samples Discussion – Description
Initial Discussion Posting:
Select and post to One (1) of the following options from either Unit 5 or Unit 6 Topics for your discussion posting. Alternatively, you can post on a topic of your own creation, related to these chapters (following similar guidelines).
Unit 5 Topics:
1 – Covariance vs. Correlation
Discuss some ways that the concepts of Covariance and Correlation are similar or different. In particular, how does the notion of Variance provide a special case for the concept of Covariance?
2 – Enabler of Statistics
Some might argue that without the Central Limit Theorem we really couldn’t do much of what we try to do with statistics.
Discuss how and why someone could make such a statement. In what ways does the Theorem enable us to perform statistical analysis that otherwise wouldn’t be available? Do you agree with the conjecture?
Unit 6 Topics:
3 – Minimum Variance Unbiased Estimator
Explain and discuss why engineers usually want the minimum variance unbiased estimator (MVUE). What benefits are achieved by using the MVUE in making engineering decisions, and what risks or impacts might be seen if another estimator is chosen at times? Try to use hypothetical examples to illustrate your thinking.
4 – Nesting Point Estimates
Point estimates often need to be nested in layers of analysis, and it is the Invariance Principle that provides a pathway for doing so. An example would be estimating Mu after having to estimate Alpha and Beta for some distributions. In simpler statistics class exercises (like those we’ve seen up until now), this is typically avoided by providing the lower level parameters within exercises or problems (e.g. asking you for Mu by giving you the Alpha and Beta). The only real options we’ve had prior to this unit for estimating lower level parameters has been trial-and-error: collecting enough data to form a curve that we then use probability plots against chosen parameter values until we find a combination of parameters that “fits” the data we’ve collected. That approach works in the simplest cases, but fails as our problem grows larger and more complex. Even for a single distribution (e.g., Weibull) there are an infinite number of possible Alpha-Beta combinations. We can’t manually test them all.
Point estimation gets us around all of that by providing the rules needed to actually calculate lower level parameters from data. We sometimes need to be able to collect a lot more data to use this approach, but it’s worth it. We’ll be able to calculate more than one possible value for many parameters, so it’s important that we have rules for selecting from among a list of candidates.
Discuss what some of those rules are, and how they get applied in your analysis. If an engineering challenge includes “more than one reasonable estimator,” (Devore, p. 249, Example 6.1 in Section 6.1) how do engineers know which to pick, and what issues arise statistically and in engineering management when making those choices?
5 – Estimation Beyond Statistics
The statistical tools in this unit help us estimate individual data points needed in our engineering analysis from other data available to us. The point estimate is typically another parameter value, such as a population mean, or process proportion. As engineers, we sometimes need to apply this kind of thinking to larger-scaled functional engineering. We might need an estimate of the risk level of a process design, which isn’t itself a statistical parameter. We might use statistical techniques to point estimate several parameters that feed into that discussion, but the final leap from those parameters might be more logic than statistics. We use our statistical intuition to make that logical decision as engineers. The decision isn’t a statistical point estimate, rather, it is an engineering point judgement.
Discuss some ways in which you expect to be able to make an engineering judgement by applying things you’ve learned in this class to situations that aren’t actually or technically statistical in nature. How will you use these statistical concepts in your general engineering work?
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