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Suppose you have two covariance matrices A and B. Is AB also a covariance matrix? Suppose that, by plain dumb luck, we also have that AB=BA. Is AB a covariance matrix under this additional condition?10 Answers
I suppose it's clear from how I wrote the question that the answer to the first question is no (for you: why?). For the second question, this is a little bit harder if you aren't experienced in linear algebra. I actually have a PhD in algebra, and the interviewer also had a PhD in algebra, so on some level this question might have been specifically targeting my background. There is a standard result that applies here; see if you can figure it out.
1. no 2. no, give an example where diagonal positivity is not true.
1 is correct, 2 is wrong. Try again. :)
2. Just checked Wikipedia, AB is cov matrix because it is symmetric semi positive definite. Is it right?
If AB=BA then yes it is symmetric. So the question boils down to: Is it in fact positive semi-definite? Why or why not? Work through that and you have your answer. My hint: Take a look at some results related to diagonalizing matrices that commute with each other.
Hi for your telephone interview with doug, what was the focus for technical interview parts, everything from math, finance, programming? or mainly probability type of question? thanks
I remember it being mostly probability and finance. Nothing too terrible.
Hi Mr.interview candidate, what were the types of finance questions Doug asked? Thanks!
Hi, Mr. interview. Do you remember what kind of data analysis example was for on-site interview? If so, can you share a little bit? What was the level of difficulty? Thanks!
1, no 2, yes