
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

use the complement
$\displaystyle P(Y_n\ge .99)=1P(Y_n< .99)=1\left[P(X_1<.99)\cdots P(X_n<.99)\right]$
$\displaystyle =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
