Recent content by tiger2030

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    Probability/Moment Generating Function

    Where do I start in showing that (1/y)ety-ln(y)2/(2σ2)+2μln(y)/(2σ2) does not converge?
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    Probability/Moment Generating Function

    Homework Statement Let X ~ Normal(μ,σ2). Define Y=eX. a) Find the PDF of Y. b) Show that the moment generating function of Y doesn't exist. Homework EquationsThe Attempt at a Solution For part a, I used the fact that fy(y) = |d/dy g-1(y)| fx(g-1(y)). Therefore I got that fy(y)=...
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    Distributing 5 different letters into 3 boxes

    I know see that 35 would have been the easiest way to go about this because letter 1 has three options, letter 2 has three options, and so on, giving you 3*3*3*3*3. For the way I did it, in order to make the result number come out I know that I have an extra 'x2' or '(2C1)' factor in case 4...
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    Distributing 5 different letters into 3 boxes

    Homework Statement How many ways can 5 different letters be posted in 3 boxes, if any number of letters can be posted in all of the three post boxes? Homework Equations Order of the letters being put into the box doesn't matter, only which letter or letters ends up in which box. A box...
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    Show k-linear forms on an n-dimensional space have dimension n^k

    I understand there would be nk different permutations of the coefficients indices but is this enough to prove the dim?
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    Show k-linear forms on an n-dimensional space have dimension n^k

    The explanation of the notation cleared a lot of stuff up for me. So I get know that we have taken apart each yj and are multiplying the coefficients together but how does this show the dimension is nk?
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    Show k-linear forms on an n-dimensional space have dimension n^k

    Ok, that clears things up a lot more. So instead I would get the coefficient with the first basis vector from y1 multiplied by the coefficient with the second basis vector from y2, and so on until it it multiplied by the coefficient with the nth basis vector from yn
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    Show k-linear forms on an n-dimensional space have dimension n^k

    ok so I am just going to try and use an example to see where my thought process is wrong and then use that to apply to a general case. Say y2=3x1+2x2+4x3. Then fj2(y)=fj2(3x1+2x2+4x3)=fj2(3x1)+fj2(2x2)+fj2(4x3)=2
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    Show k-linear forms on an n-dimensional space have dimension n^k

    That would equal ∑ai, where yi=∑aixi
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    Show k-linear forms on an n-dimensional space have dimension n^k

    Say x31=αe1+βe2+γe3. Then fj1(x31)=fj1(αe1+βe2+γe3)= αfj1(e1)+βfj1(e2)+γfj1(e3)=α+β+γ?
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    Show k-linear forms on an n-dimensional space have dimension n^k

    so fjk(∑αiei)=∑aiδi=∑ai?
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    Show k-linear forms on an n-dimensional space have dimension n^k

    As a linear combination of basis elements?
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    Show k-linear forms on an n-dimensional space have dimension n^k

    so all fjk map to either 1(for fjk(xik)) or 0(for fjk(xim), where k≠m. also, if xik=yik, then fjk(xik)=1=fjk(yik) Therefore all f are well defined.
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    Show k-linear forms on an n-dimensional space have dimension n^k

    Ok so first I need to check that they are well defined k-linear forms, correct?
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    Show k-linear forms on an n-dimensional space have dimension n^k

    Yes, this makes sense because to be linear, you must be able to pull the constant out and still yield the same answer.
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