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Math Help - Help! Theoretical Stats

  1. #1
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    Help! Theoretical Stats

    Can anyone help me solve this problem??

    Suppose that X(subscript 1),....,X(subscript n) form a random sample from a unifom distribution on the interval [0,1] and that the random variable Y(subscript n)= max{X(subscript 1),....,X(subscript n)}.
    Determine the smallest value of n such that Pr[Y(subscript n)≥.99]≥.95
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  2. #2
    MHF Contributor matheagle's Avatar
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    use the complement

    P(Y_n\ge .99)=1-P(Y_n< .99)=1-\left[P(X_1<.99)\cdots P(X_n<.99)\right]

     =1-\left[P(X_1<.99)\right]^n=1-\left[.99\right]^n

    now set this greater than or equal to .95, take the log... blah blah
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  3. #3
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    thanks for you help!!
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