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October 6th, 2017, 05:56 PM   #1
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Question Do you recognize this distribution?

At part C, I obtain the marginal density functions to be:
f(x) = 3x - (3/2)x^2 on [0, 1], 0 elsewhere.
f(y) = 3y^2 - 6y +3 on [0, 1], 0 elsewhere.

However, the question proceeds to ask if I recognize these distributions. I assume that I'm supposed to recognize them, but I'm struggling to. I notice that if I factor some terms, I can sort of get it to look like the Beta distribution, but it's not quite right. As a result, I have no idea how I'd write the parameterized version of it. If it's related to some other distribution, I'm not quite sure which one. Do you recognize this distribution? (Or did I perhaps calculate the marginal density functions incorrectly?)
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October 6th, 2017, 06:05 PM   #2
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I think you need to redo the marginals.

I get

$f(x) = 3(1-2x+x^2),~x\in [0,1]$

$f(y) = 6y(1-y),~y\in [0,1]$
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October 6th, 2017, 06:50 PM   #3
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You're right. I misinterpreted one of the inequalities and integrated over the wrong region. From that point, the rest is straightforward. Thank you for helping me catch the error.

Last edited by skipjack; October 7th, 2017 at 01:46 AM.
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