Suppose That a Bag Contains Six Slips of Paper: One

Question

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The Answer is The expected value is

\frac { 1 } { 6 } \cdot 1 + \frac { 2 } { 6 } \cdot 2 + \frac { 3 } { 6 } \cdot 3 = \frac { 14 } { 6 }

. To compute the variance we compute

E \left( X ^ { 2 } \right) - E ( X ) ^ { 2 }

, where

X

is the value on the slip. We have

E \left( X ^ { 2 } \right) = \frac { 1 } { 6 } \cdot 1 + \frac { 2 } { 6 } \cdot 4 + \frac { 3 } { 6 } \cdot 9 = \frac { 36 } { 6 } = 6

, so

V ( X ) = 6 - \left( \frac { 14 } { 6 } \right) ^ { 2 } = \frac { 5 } { 9 }

.

Essay