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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is

    A)  5                                            

    B)  6

    C)  4                                            

    D)  none of these

    Correct Answer: C

    Solution :

                    In binomial distribution mean\[=np,\]variance \[=npq.\] Given \[np=4,\text{ }npq=3\] \[\Rightarrow \]               \[q=\frac{3}{4}\]                 \[p=1-\frac{3}{4}=\frac{1}{4}\] Mode is an integer\[x\]such that \[np+p>x>np-p\] \[\Rightarrow \]               \[4+\frac{1}{4}>x>4-\frac{3}{4}\] \[\Rightarrow \]               \[3.25<x<4.25\] \[\therefore \]  \[x=4\]


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