- #1

Master1022

- 611

- 117

- Homework Statement
- What is the expected value of the median of three dice rolls?

- Relevant Equations
- Expected Values

Hi,

I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand.

"

I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand.

**Question: Calculate the expected value of the median of rolling a die three times.**

Attempt:I read the following answer on math stack exchange hereAttempt:

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*As already noted in a comment, the result can be derived from symmetry without any calculation. The probability distribution of the die is invariant under the symmetry transformation ##x \rightarrow 7 - x##, a reflection about ##x = \frac{7}{2}##. Thus the median and the mean must also be invariant under this transformation. Thus they must be the centre of the reflection, [itex] x =\frac{7}{2} [/itex]*. "I don't quite understand why this means the median of rolling three die is ##\frac{7}{2}##. I apologize if this is quite obvious, but any help would be appreciated