Help! Theoretical Stats

May 2010
11
0
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
 

matheagle

MHF Hall of Honor
Feb 2009
2,763
1,146
use the complement

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

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

now set this greater than or equal to .95, take the log... blah blah