# Help! Theoretical Stats

• May 10th 2010, 04:48 PM
uva123
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
• May 10th 2010, 06:41 PM
matheagle
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
• May 10th 2010, 06:56 PM
uva123
thanks for you help!!