I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.
I am a PhD educated mathematician working in research at a major university.
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.
BA mathematics & physics, PhD mathematics from a top 20 US school.
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.
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The least-squares method can be used to produce a line-of-best-fit for a set of data. If you are given a line that is a potential best fit, you would find the residual at each data point (the height from
This is actually a very tricky question, so let's start with an easier version. Let's roll a 4-sided die (labeled A, B, C, D) 10 times. Say we want to figure out the probability of getting all four
This is a very basic, standard concept. Here's how it works: First, if you did this one time, the probability of guessing it right is one in five. We will call that "p" -- so we say p=1/5. And
The key to determining whether the problem is asking you to count combinations or permutations is whether order matters. A permutation accounts for order, while a combination does not. The problem states
Assuming the payout is the same, then yes, the two games are the same. Each lottery ticket is (essentially) independent -- they are random, so winning or losing one has no effect on the next ticket