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Math Help - Probability Proof

  1. #1
    h2p
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    Probability Proof

    x = 3p^2 − 2p^3

    Show that x < p iff p < 1/2

    note: p^2 = p'sqaured and p^3 = p'qubed

    Can someone please tell me how to start off this problem?

    thanks!
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  2. #2
    h2p
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    I probably should have just called it an algebraic proof however "p" in this case is a probability so I really should has said...

    x = 3p^2 − 2p^3

    Show that x < p iff 0 =< p < 1/2

    In other words p can be from 0 to less than 0.5

    Anyone?
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  3. #3
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    First iff notation is a two way stree, we have to go forward as well as backward.

    1st step to show x<p implies p<1/2.
    note, x is a function of p, and x or 3p^2-2p^3 are equivalent.
    for x<p, we can have 3p^2-2p^3<p
    just do some rearrengement, you can get when p>1 or p<1/2 which allow
    x<p, then we choose the p<1/2

    2nd step, go backward, show p<1/2 implies x<p.
    if we show x/p<1, then we showed x<p.
    use (3p^2-2p^3)/p, can you show this is less than 1, when p<1/2?
    of course you can.

    still having problem, please point out.
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