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If the probability of chossing an interger "k" out of 2m integers 1,2,3,….,2m is inversely proportional to k^(4)(1leklem).Ifx_(1) is the probability that chosen number is odd and x^(2) is the probability that chosen number is even, then |
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Answer» `x_(1)gt1//2` `underset(k=1)overset(2M)sum(lamda)/(k^(4))=1` `or underset(k=1)overset(2m)sum(1)/(k^(4))=1` Let `x_(1)` be the probability of choosing the odd numer. Then `x_(1)underset(k=1)overset(m)sumP(2k-1)=lamdaunderset(k=1)overset(m)sum(1)/((2k-1)^(4))` Also, `1-x_(1)=underset(k=1)overset(m)sumP(2k)` `=lamdaunderset(k=1)overset(m)sum (1)/((2k)^(4))` `ltlamdaunderset(k=1)overset(m)sum(1)/((2k-1)^(4))` `implies1-x_(1)ltx_(1)` `impliesx_(1)gt1//2` `impliesx_(2)lt1//2` |
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