a) The data obtained from a given experiment is a pair of numbers

a

and

b

, where

a \geq 0

and

b \geq 0

. It is known that

a

and

b

have mean

1

; what is the largest value that the standard deviation can be?

(b) The data obtained from a given experiment is a triple of numbers $x$ , $y$ and $z$ , where each is non-negative. It is known that the mean of $x$ , $y$ and $z$ is $1$ ; what is the largest value that the standard deviation can be?

t_{1}, \dots, t_{n}

, where each is non-negative. It is known that the mean of the

t_{j}

1

. Show that the standard deviation may be as large as

\sqrt{n - 1}