Dvds for Christmas

[BMAD]

I hate to bring up my dvds again (My old post about my dvds) but I love movies and so of course i got 6 new dvds for Christmas.  Before Christmas , i had 26 dvds in ABC order.  With each DvD starting with 1 of 26 letters in the English alphabet. After i put my new 6 dvds up, how many places to the right should i expect my "U" DvD to shift? 

[phil1882]

 

i'd say 6. if you take into account letter frequency, the letters to the left of u far outweigh the letters to the right.

Edited January 4, 2016 by phil1882

[Logophobic]

We cannot assume that the general letter frequency of the English language applies to this collection of DVDs. The only data we have, one occurrence of each letter in a collection of 26 titles, suggests a uniform distribution.

Spoiler

There are 20 letters in the range [A-T], which go to the left of the U, and 5 letters in the range [V-Z], which go to the right. There is also the U which may go to the left or to the right. Without additional information, we must assume a 50/50 split in this case. This gives us 20.5/26 to the left of the U and 5.5/26 to the right of the U. With six new DVDs, we can expect a 4.7:1.3 ratio to the left and right of the U. That is, we should expect the U DVD to shift 5 places to the right.