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KVPY Sample Paper KVPY Stream-SX Model Paper-8

  • question_answer
    The mean of, 0 1, 2, 3, ....re, with the corresponding weight \[^{n}{{C}_{0}}{{,}^{n}}{{C}_{1}}{{,}^{n}}{{C}_{2}},{{.....}^{n}}{{C}_{n}}\] is -

    A) \[\frac{{{2}^{n}}}{n+1}\]                  

    B) \[\frac{{{2}^{n+1}}}{n(n+1)}\]

    C) \[\frac{n+1}{2}\]                      

    D) \[\frac{n}{2}\]

    Correct Answer: D

    Solution :

    mean \[=\frac{\sum{{{x}_{i}}{{w}_{i}}}}{\sum{{{w}_{i}}}}=\frac{0{{C}_{0}}+1{{C}_{1}}+.....n{{C}_{n}}}{{{C}_{0}}+{{C}_{1}}+.....+Cn}=\frac{n{{.2}^{n-1}}}{{{2}^{n}}}\]


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