This is easy..... P(Y(n)>m)= 1-(0.5)^n
P(Y(n)>m)= 1-P(Y(n)<m)= 1-P(Y1<m)P(Y2<m)....P(Yn<m)=1-(0.5)^n
For the first part, just get the density or cdf of the largest order stat.
Hey can someone help me figure this out plz
If Y is a continuous random variable and m is the median of the distribution, then m is such that P(Y≤m)=P(Y≥m)=0.5. If Y1, Y2,...,Yn are independent, exponentially distributed random variables with mean β and median m then Y(n)= max(Y1, Y2,...,Yn) does not have an exponential distribution. Use the general form of FY(n)(y) to show that P(Y(n)>m)= 1-(0.5)^n.
Thanks alot !!