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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 8

  • question_answer
    Suppose \[f(x)=\frac{k}{{{2}^{x}}}\] is a probability distribution of a random variable X that can take values 0,1,2, 3, 4. Then k is equal to

    A) 16/15           

    B) 15/16

    C) 31/16               

    D) none of these

    Correct Answer: D

    Solution :

    [d]: We have, \[f(x)=\frac{k}{{{2}^{x}}}\]. Clearly, \[f(0)+f(1)+...+f(4)=1\] \[\Rightarrow \]\[k+\frac{k}{2}+.....+\frac{k}{{{2}^{4}}}=1\]\[\Rightarrow \]\[\frac{k[1-{{(1/2)}^{5}}]}{1-1/2}=1\] \[\Rightarrow \]\[\frac{k(31/32)}{1/2}=1\Rightarrow k=\frac{16}{31}\]


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