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Math Help - joint and marginal p.m.f.s

  1. #1
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    joint and marginal p.m.f.s

    In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date
    nonsmokers. 1% prefer to date smokers, and 21% donít care. Suppose seven such boys are
    selected randomly and X equals the number who prefer to date nonsmokers and Y equals the
    number who prefer to date smokers.

    (a) Determine the joint p.m.f. of X and Y. Be sure to include the support of the p.m.f.

    (\frac{7!}{x!7-x!})*(\frac{7-x!}{y!7-x-y!})*(0.78^{x})*(0.01^{y})*(0.21)^{7-x-y}?

    (b) Find the marginal p.m.f. of X. Again, include the support.

    (\frac{7!}{x!7-x!})*(0.78^{x})*(0.21)^{7-x-y}?

    Thank you!
    Last edited by redpack; May 20th 2009 at 06:34 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    (a) looks right, but you need to place () before the factorials and cancel that common term. This is a multinomial.
    (b) does not make sense mathematically. You can't have y in a function that is only a function on x. This is just a binomial.
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  3. #3
    MHF Contributor matheagle's Avatar
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    Here are my corrections.......


    Quote Originally Posted by redpack View Post
    In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date
    nonsmokers. 1% prefer to date smokers, and 21% don’t care. Suppose seven such boys are
    selected randomly and X equals the number who prefer to date nonsmokers and Y equals the
    number who prefer to date smokers.

    (a) Determine the joint p.m.f. of X and Y. Be sure to include the support of the p.m.f.

    \frac{7!}{x!y!(7-x-y)!}(0.78)^x(0.01)^y(0.21)^{7-x-y}

    (b) Find the marginal p.m.f. of X. Again, include the support.

    \frac{7!}{x!(7-x)!}(0.78)^x(0.22)^{7-x} where x=0,...,7.

    Thank you!
    You combine the .21 and the .01 for the q in the 'failure' category.
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  4. #4
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    In part b, you can combine the 0.01 and 0.21 and just forget the y? the exponent doesn't make a difference?
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  5. #5
    MHF Contributor matheagle's Avatar
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    a function of just x can only have constants and x's, no other variables.
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  6. #6
    MHF Contributor matheagle's Avatar
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    IN (b) a success is to prefer to date nonsmokers, so p=.78 and q=.22
    The complement is {don't care or date smokers}.
    Last edited by matheagle; May 20th 2009 at 11:12 PM.
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