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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer
    A random variable X has the following probability distribution: X: 0  1   2   3   4   5   6   7   8 P(X=x): a  3a  5a  7a  9a  11a  13a  15a  17a Then the value of a is:

    A) \[\frac{7}{81}\]                         

    B) \[\frac{5}{81}\]

    C) \[\frac{2}{81}\]                         

    D) \[\frac{1}{81}\]

    Correct Answer: D

    Solution :

    [d] We must have \[a+3a+5a+7a+9a+11a+13a+15a+17a=1\] \[\therefore \frac{9}{2}\left( a+17a \right)=1\] [\[\therefore \]sum of the probability = 1]             Or \[\frac{9\times 18a}{2}=1\]                \[\therefore a=\frac{2}{9\times 18}=\frac{1}{81}\]


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