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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    If\[X\]is a binomial variate with the range\[\{0,\,\,1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6\}\]and\[P(X=2)=4P(X=4),\]then the parameter\[p\]of\[X\]is

    A) \[\frac{1}{3}\]

    B)                                        \[\frac{1}{2}\]

    C) \[\frac{2}{3}\]                   

    D)        \[\frac{3}{4}\]

    Correct Answer: A

    Solution :

    Here,\[n=6\] According to the question                 \[^{6}{{C}_{2}}{{p}^{2}}{{q}^{4}}=4{{\cdot }^{6}}{{C}_{3}}{{p}^{4}}{{q}^{2}}\] \[\Rightarrow \]               \[{{q}^{2}}=4{{p}^{2}}\] \[\Rightarrow \]               \[{{(1-p)}^{2}}=4{{p}^{2}}\] \[\Rightarrow \]               \[3{{p}^{2}}+2p-1=0\] \[\Rightarrow \]               \[(p+1)(3p-1)=0\] \[\Rightarrow \]               \[p=\frac{1}{3}\]                 (\[\therefore \,\,p\]cannot be negative)


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