Recent content by jakemf1986

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A simple computational question, that I saw in a journal article and have been having trouble getting. Define the variable V (implicitly) by: V=b + \int^{rV}_{0} rV dF(s) + \int^{\infty}_{rV} s dF(s), where r is a constant and F has support on [0,∞). Question: Show that...

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This is not actually a homework question but something I saw in a (economics) journal article and have been having trouble getting. It's very simple so I thought I'd post it here. Define the variable V (implicitly) by: V=b + \int^{rV}_{0} rV dF(s) + \int^{\infty}_{rV} s dF(s), where r...

Thanks all for the replies. Let me clarify: V is the set of vectors whose largest entry *must* be 1 and whose smallest entry *must* be 0. So if for example m = 2, so that we're restricting attention to 2-dimensional vectors, then V would consist of exactly two vectors, namely (0,1) and...

Hm I suppose what I really want is: If you give me any v_1, v_2, ..., v_n ∈ V, I can conclude with probability 1 that the following set of vectors is LI: {σ, v_1, v_2, ..., v_n}. Thank you!

Restrict attention to vectors in ℝ^m where m is a natural number. Let σ be the vector of ones. Let V be the set of vectors whose largest entry is 1 and whose smallest entry is 0. When is it (generically) the case that the set of vectors {σ, v_1, v_2, ..., v_n} is linearly independent...