expected value of a random palindrome If you choose a 6-digit palindrome at random, what is the expected value for the number? 
All possible palindromes are equally likely to be chosen. Beginning number must be NONZERO, so numbers like 012321 are NOT allowed.
I'm not sure where to start. What values and the probabilities of the values should I look at? 

There are 9 choices for the first digit, and 10 choices each for the second and third digit.  There is an equal probability of each of these $900$ numbers.
So you want: $\sum\limits_{f=1}^9 \sum\limits_{s=0}^9\sum\limits_{t=0}^9 \left(\dfrac{100001\; f+10010\;s+1100\;t}{900}\right)
\\ = \dfrac{100001\left(\sum\limits_{f=1}^9 f\right) \left(\sum\limits_{s=0}^9\sum\limits_{t=0}^9 1\right)+11110\left(\sum\limits_{f=1}^9\sum\limits_{k=0}^9 1\right) \left(\sum\limits_{h=0}^9 y\right)}{900}$
Can you complete?
