Probability of seeing a heterozygote using Hardy-Weinberg












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This question is an extension of this question.



The hardy-weinberg equation is defined as, given two alleles, $A$ and $a$, and $frequency(A) = p$ and $frequency(a) = q$. Now, we have $p+q = 1 = p^2 + 2pq + q^2$.



Now, based on the linked question, I know what the probability of a heterozygote is for when there are only two alleles. But that answer uses a guess and check approach. How do I generalize this for $n$ alleles situation using an equation?



For current intuition is the following, if there are $n$ alleles, then I would use the multi-normial theorem to expand the allele probabilities then use that information to figure out the maximum possible probability. But now sure how to proceed.










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$endgroup$

















    0












    $begingroup$


    This question is an extension of this question.



    The hardy-weinberg equation is defined as, given two alleles, $A$ and $a$, and $frequency(A) = p$ and $frequency(a) = q$. Now, we have $p+q = 1 = p^2 + 2pq + q^2$.



    Now, based on the linked question, I know what the probability of a heterozygote is for when there are only two alleles. But that answer uses a guess and check approach. How do I generalize this for $n$ alleles situation using an equation?



    For current intuition is the following, if there are $n$ alleles, then I would use the multi-normial theorem to expand the allele probabilities then use that information to figure out the maximum possible probability. But now sure how to proceed.










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      This question is an extension of this question.



      The hardy-weinberg equation is defined as, given two alleles, $A$ and $a$, and $frequency(A) = p$ and $frequency(a) = q$. Now, we have $p+q = 1 = p^2 + 2pq + q^2$.



      Now, based on the linked question, I know what the probability of a heterozygote is for when there are only two alleles. But that answer uses a guess and check approach. How do I generalize this for $n$ alleles situation using an equation?



      For current intuition is the following, if there are $n$ alleles, then I would use the multi-normial theorem to expand the allele probabilities then use that information to figure out the maximum possible probability. But now sure how to proceed.










      share|cite|improve this question









      $endgroup$




      This question is an extension of this question.



      The hardy-weinberg equation is defined as, given two alleles, $A$ and $a$, and $frequency(A) = p$ and $frequency(a) = q$. Now, we have $p+q = 1 = p^2 + 2pq + q^2$.



      Now, based on the linked question, I know what the probability of a heterozygote is for when there are only two alleles. But that answer uses a guess and check approach. How do I generalize this for $n$ alleles situation using an equation?



      For current intuition is the following, if there are $n$ alleles, then I would use the multi-normial theorem to expand the allele probabilities then use that information to figure out the maximum possible probability. But now sure how to proceed.







      probability






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 22 at 8:22









      JonathanJonathan

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