KVPY SX SB Exam 2013 Question Paper

Let n ≥ 3. A list o f numbers has mean µ and standard deviation σ. A new list of numbers is made as follows: ${\mathit{y}}_1=0,{\mathit{y}}_2={\mathit{x}}_2,....,{\mathit{y}}_{\mathit{n}-1},$ ${\mathit{y}}_{\mathit{n}}={\mathit{x}}_1+{\mathit{x}}_{\mathit{n}}$. The mean and the standard deviation of the new list are $\hat{\mathit{\mu }}$ and $\hat{\mathit{\sigma }}$. Which of the following is necessarily true?