Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Random Variables & Distribution Functions
Let \(X_1, X_2, ..., X_n\) be i.i.d.(independent and identically distributed) random variables with uniform distribution on the interval [0, 1]. Let \(Y_{n,k} \)denote the kth order statistic based on the sample \(X_1, X_2, ..., X_n\). If we select two different samples of size 25 and 26, denoted as\( X_{25,1}, X_{25,2}, ...., X_{25,25 }\)and \(X_{26,1}, X_{26,2},....X_{26,26}\) respectively, and let Y be the 8th order statistic in both samples. What is the probability that \(Y_{25,8} = Y_{26,8}\)?
1
0
2
\(\frac{1}{26}\)
3
\(\frac{1}{25}\)
4
It cannot be determined.