Independent And Stationary Sequences Of Random Variables - Chapter 7 potx

~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~ ~~~ ~~~~~ ~ ~~~~~~~~~~ ~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~~~ ~~~~~~ ~~~~~~~~ ~ ~ ~~ ~~ ~~~ ~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~ ~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~ ~ ~ ~~~ ~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~ ~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~ ~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~ ~ ~ ~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~ ~~~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~ ~ ~~~~ ~~~ ~ ~~~ ~ ~~~~~~~ ~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~ ~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~ ~ ~~~~~~ ~~ ~~~ ~~~~ ~~ ~ ~~~~~ ~~ ~ ~ ~ ~~ ~~ ~~~ ~ ~~ ~~~ ~~~~~ ~ ~~ ~~~ ~ ~~~~ ~ ~ ~~ ~~ ~~~ ~~ ~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~ ~~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~ ~~~~~~~~ ~~~~~~~ ~~~ ~~~~~~~~~~~~ ~~ ~ ~~~ ~ ~~ ~~ ~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~ ~~~~~~~~~ ~~ ~~ ~ ~~ ~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~ ~~ ~ ~ ~~~~~~~~~ ~~~~~~~~~ ~~~~~ ~~ ~~~~~~~~~~~ ~~ ~~ ~~~~~~~~~~ ~~~~ ~~~~~~~~~~~~~ ~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~~ ~~ ~~~ ~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~ ~ ~ ~~~~~~~~~ ~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~ ~ ~~~~~~~~~~~~~~ ~ ~~~~~~~ ~ ~~ ~~~~~~~~~~ ~~ ~~~~~~ ~~ ~~~ ~ ~ ~~~~~~~ ~ ~~ ~~ ~~~ ~~~~~~~ ~~~ ~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~ ~ ~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~ ~ ~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~ ~ ~~~~~~~~~~ ~~~~~~~~~~~~ ~~ ~~~~~ ~~~~~ ~ ~~ ~~ ~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~ ~~~~~~~~~ ~~~~ ~~~~~~~ ~~ ~ ~ ~~~ ~ ~~~~ ~~~~~~~~~~~~ ~ ~ ~ ~ ~~~ ~~ ~~~ ~ ~~ ~ ~ ~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~~~ ~~~ ~ ~~~~~ ~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~~~~~~~~~~ ~ ~~~~~ ~~~ ~ ~~~~~~~~~~~~~~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~ ~~~~~~~ ~~ ~~~ ~~~~~~ ~~~~ ~ ~~~ ~~~~ ~~~ ~~ ~~ ~ ~~~~~~ ~ ~ ~ ~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~ ~~~~~~~~~~~ ~~~~~~~~~~~ ~~~~~~~~~~~~~ ~~~~~~~ ~~~~~~~~~~~~~~~ ~~~~ ~~~~ ~~ ~~~~~~~ ~ ~~ ~~~ ~~ ~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~ ~~~ ~~ ~~ ~~~ ~~~~ ~ ~~~~~~~~~~~~~~ ~~ ~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~ ~~~~~~ ~ ~~~ ~~ ~~~ ~ ~~~~~ ~~~~~ ~~ ~ ~~~~~~~ ~ ~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~ ~~~~~ ~ ~~ ~ ~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~ ~~ ~~~ ~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~ ~~~~~ ~~~~ ~ ~ ~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~ ~~~~~~ ~ ~ ~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~ ~~~~~~~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~ ~~~~~~~~~ ~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~ ~~ ~~~ ~~~ ~~~~~~~~~~~~~ ~~~~~~ ~~~~~~ ~ ~~~~ ~~~ ~ ~~ ~~ ~~~ ~~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~ ~ ~~~~~ ~ ~ ~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~ ~ ~ ~ ~ ~ ~ ~ ~~~~~ ~ ~~ ~~ ~~~ ~~~ ~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~ ~~~~~ ~ ~~~ ~ ~ ~~ ~ ~~~ ~~~~~ ~~~~ ~ ~~ ~ ~~ ~ ~~~~~ ~ ~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~ ~ ~ ~~~~~~~~~~~~~~~~~~ ~ ~ ~ ~~~~~~~~~~~~~~ ~~ ~~ ~~~~ ~~~~~~~~~~~~~~ ~~~~~ ~~~~~ ~~~~~~~ ~~~~~ ~~ ~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~ ~~~~~~ ~ ~~ ~~~ ~ ~~ ~~ ~~~ ~~ ~~ ~ ~ ~ ~ ~ ~ ~ ~~~~ ~~~~~~ ~ ~~~~ ~~~ ~ ~ ~~~ ~~ ~ ~ ~ ~~~~~ ~~ ~~~~~ ~ ~ ~ ~ ~ ~~ ~ ~ ~~ ~~ ~~~ ~~ ~~ ~~~~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~ ~ ~~~~~ ~ ~~~~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~ ~~~~~~~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~ ~ ~~ ~~ ~~~~ ~~~~~ ~ ~ ~ ~ ~~ ~ ~ ~~~ ~ ~~~ ~ ~ ~ ~~ ~~~~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~ ~ ~ ~~~~~~~ ~~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~ ~~ ~~ ~~~~ ~~ ~~~~~~~~~~ ~ ~ ~ ~ ~ ~ ~~~~ ~~~ ~~ ~~~~ ~~~~ ~~ ~ ~~ ~ ~~ ~~~~~~~~ ~~~~ ~~ ~ ~~~ ~ ~ ~ ~ ~~ ~~~~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~ ~~~ ~~~~~~~ ~~~~~ ~ ~~~ ~~~~~ ~ ~~~~~~ ~ ~ ~~~~ ~ ~~~~ ~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~ ~~ ~~~~ ~ ~~ ~ ~ ~ ~ ~ ~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~ ~ ~~~ ~ ~~ ~~ ~~~~ ~~ ~ ~ ~~~ ~ ~ ~ ~~~~~~~~~ ~~~~ ~~ ~~ ~ ~~ ~ ~~~~~ ~~ ~~ ~ ~~~~~~~~~ ~ ~ ~~ ~~ ~~~~ ~~~~~~~~~~~~~ ~ ~ ~ ~~~~~~~~~~~~ ~ ~~ ~ ~~~ ~ ~~ ~~ ~~~~ ~ ~ ~~ ~ ~ ~~~ ~ ~ ~ ~~~~~~~~~ ~~~~ ~~ ~~~ ~ ~~~~ ~~~~~ ~~ ~~ ~ ~ ~~~~~~~~~ ~ ~ ~~ ~~ ~~~~ ~~~~~~~~~~~~~ ~~~ ~~ ~ ~~~~~~~~~~~ ~ ~~ ~ ~~~ ~ ~~ ~~ ~~~~ ~~~ ~~~ ~~ ~ ~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~~ ~ ~~~~~~ ~~ ~~~~~ ~~ ~~~ ~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~ ~~ ~~ ~~ ~ ~~ ~ ~ ~ ~ ~ ~~ ~~~~ ~~~~~ ~ ~~ ~ ~ ~ ~~~ ~~~~~~~ ~~~ ~~~~~~~~ ~~ ~~~~~ ~ ~ ~~~~~~~ ~ ~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~ ~ ~~~ ~~~ ~ ~ ~ ~~~~ ~~~~ ~~~~ ~ ~ ~~ ~~ ~~~~ ~~ ~ ~ ~ ~~~~~~~~~ ~~~~ ~ ~~~ ~~~ ~ ~~~~~~~~ ~ ~~ ~~~~~~~~~ ~ ~ ~ ~ ~~ ~~ ~~~ ~~~~~ ~~ ~~ ~~~~~ ~~~~~~~ ~~~~ ~ ~~~ ~~~~~~ ~ ~ ~ ~~ ~~~~~~~ ~ ~~ ~~ ~~~~ ~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~ ~~~~~ ~ ~ ~ ~~~ ~ ~~ ~~ ~ ~ ~~ ~ ~~~~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~ ~~~~ ~~ ~~ ~~~~~ ~~~~~ ~ ~~~ ~ ~ ~ ~~~~~~~~ ~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~ ~~~ ~~~ ~ ~~~~~~~ ~ ~ ~~~~ ~ ~~~~ ~~~~~ ~~~ ~~~~~~~~ ~ ~ ~ ~ ~ ~~~~~ ~ ~ ~ ~ ~ ~ ~~ ~~~~ ~~~ ~ ~ ~~~~~~~~ ~ ~~~~~~~~~~~~ ~ ~ ~ ~ ~~~ ~~ ~ ~~~ ~~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~ ~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~ ~~ ~~~ ~ ~~~~~~~~ ~ ~ ~~~~~~ ~ ~ ~ ~ ~ ~ ~~ ~~ ~~~~ ~ ~ ~ ~ ~~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~~~~ ~ ~~~~ ~ ~ ~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~ ~~ ~~~~~~~~~ ~~ ~~ ~~~~~ ~~~~~~~~~ ~ ~~~~~~~ ~ ~~~~~~~ ~ ~~~ ~~~ ~ ~~~ ~ ~~ ~ ~ ~~ ~ ~~~~ ~~ ~ ~ ~~~ ~~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~~~~~~ ~ ~~~~~~~~~~ ~ ~~~ ~~ ~ ~~~ ~~~ ~ ~~~ ~ ~~ ~~~~~~~ ~~~~ ~ ~ ~~~ ~~~~ ~ ~~~ ~ ~~ ~ ~~~~~~~~ ~~~ ~~~~~ ~ ~ ~~ ~ ~ ~ ~ ~~ ~~~~ ~~~ ~~~ ~~~~~~~ ~ ~ ~ ~ ~ ~~~~~~~~~~~ ~~~~ ~ ~~~ ~~~~ ~~ ~~ ~~~~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~ ~~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~~~~~~ ~ ~ ~~~~ ~~ ~ ~ ~~ ~~ ~~~~~~ ~~~~ ~ ~ ~~~ ~~~~~~~ ~ ~~~ ~ ~ ~~~~~~~~~~~~~~~ ~ ~ ~~ ~ ~ ~~~~ ~~~ ~ ~ ~ ~ ~ ~~~ ~~~ ~~ ~~~~~~~~ ~ ~~~~ ~ ~ ~~~ ~~ ~ ~~~~~~~ ~ ~~~ ~ ~ ~~ ~ ~ ~ ~ ~ ~~ ~~~~~ ~~~~~ ~ ~ ~ ~ ~~~~~ ~ ~ ~~~~~~~~ ~~~ ~ ~~~ ~ ~~ ~ ~ ~~~ ~ ~ ~~~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~ ~~~~~~~~~~~ ~~~~~ ~~~~ ~ ~~~~~~~~ ~ ~~~~~ ~ ~~~~ ~~ ~~~ ~ ~~ ~~~~ ~~ ~ ~~~~~~ ~~~~~~ ~ ~~ ~ ~ ~ ~~~~~~~~ ~ ~~~~~~~~ ~~ ~~~ ~ ~~~~~~ ~ ~~ ~~~~ ~ ~~~~~~ ~ ~~ ~ ~~~~~~ ~~ ~~~ ~ ~ ~~~~ ~~ ~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~ ~ ~ ~~ ~~ ~~~ ~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~ ~~~~~~~~~~ ~ ~~ ~ ~~~~~~ ~~ ~~~ ~ ~~ ~ ~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~ ~~~~~~~~~~~ ~~ ~ ~~~~~~~~~ ~~~ ~~~ ~~~~~~~~~ ~ ~~~~~~~~~~~ ~~ ~~~ ~ ~~ ~ ~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~ ~~ ~~ ~~~~~ ~~~~~~~~~~~~~~ ~~~ ~ ~ ~~~ ~ ~~~ ~ ~~~~~~~~~~ ~~ ~~~ ~ ~~ ~ ~ ~~ ~~ ~~~ ~~~~~~~~~~~~ ~~ ~~ ~~~~~~~~~ ~~~~~~~ ~ ~ ~ ~~~~ ~ ~ ~~ ~ ~~~~ ~ ~ ~ ~ ~~ ~~~ ~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~ ~~~~~~~~~~~ ~~ ~~~ ~ ~~~ ~~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~ ~~~~~ ~ ~~ ~~~ ~ ~~~~ ~ ~ ~~~ ~ ~ ~~ ~ ~~~~ ~ ~~~~~~~~~~~~~~ ~ ~ ~ ~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~~~~ ~ ~~~ ~ ~ ~~ ~ ~ ~ ~~~~~ ~ ~ ~ ~ ~~ ~ ~~~~ ~ ~~ ~~~ ~~~~ ~ ~~~ ~ ~~~~~~~~~~~~~ ~ ~~~~~~~ ~~ ~~ ~~~~ ~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~ ~~ ~~~~~~ ~~ ~~ ~~~ ~~~~~~~ ~ ~ ~~ ~ ~ ~ ~ ~~~~~~~ ~ ~~ ~~ ~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~ ~ ~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~ ~~ ~ ~~ ~~~~~~~~ ~~ ~~~~ ~ ~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~ ~~~~~~~~~~~~ ~~~~~~~~~~~~ ~~~~ ~ ~~~ ~~~ ~ ~~~~~~~~ ~ ~~~~~~~~~~ ~~~~~~~~~~~~ ~~ ~ ~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~ ~~~ ~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~ ~ ~~ ~~~ ~ ~ ~~ ~~~~ ~~~~~~~~~~~~~~~~~~~ ~~~ ~ ~ ~~ ~~~~ ~~~~~~~~~~~~~~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~ ~~ ~ ~~~~~~~~~~~~ ~~ ~~~~~~~~~ ~~~ ~ ~~ ~ ~ ~ ~ ~~~ ~~~~~~~~~~~~ ~ ~ ~~ ~~ ~~~ ~~~~~ ~~~~~~~~~~ ~~~~~ ~ ~~~ ~~~~~~~~~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~ ~~~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~~~~~~~~~~~~ ~ ~~~~~~ ~~~ ~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~ ~ ~~~~~~~~~~~~~~ ~ ~~~ ~ ~~~~ ~ ~ ~ ~~~~~~ ~~~ ~~ ~~~~~~~~~~ ~ ~ ~~ ~~ ~~~ ~~~~~~ ~~~~~~~~~~~~ ~ ~~ ~~~~~~~~~ ~~~~~~~~ ~~ ~~ ~~~ ~~~~~~ ~~~ ~ ~~ ~ ~~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~~~~~ ~ ~~~ ~ ~ ~~ ~~~~~~~~ ~ ~~~~~~~ ~~~~ ~ ~ ~ ~~~~~~ ~~~ ~~~ ~ ~ ~~~~~~~~~ ~~ ~ ~ ~~ ~~ ~~~ ~ ~ ~~~ ~~~~~~~ ~~~ ~~~ ~ ~ ~~~~~~~~~~ ~~~~ ~~~~~~~ ~ ~ ~~~~~~ ~~~~~~~~~~ ~ ~~~~~ ~ ~~~~~~ ~~~~~~ ~~~~~~~~~~~ ~ ~ ~ ~ ~~ ~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~ ~ ~~~~~ ~ ~~~~~ ~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~ ~~~~ ~~~ ~~~ ~ ~~ ~~ ~~~ ~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~ ~~~~ ~~~ ~~ ~~ ~~~ ~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~ ~~ ~~ ~~~~ ~ ~~~ ~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~ ~ ~~~~~~ ~~~ ~~ ~~~~~~~~~ ~ ~ ~ ~ ~~ ~~~ ~ ~ ~~~~ ~~~~ ~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~ ~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~ ~~ ~~ ~~~~ ~~~~~~~~~~~ ~~~~~ ~ ~ ~ ~ ~~~~~ ~~~~~~~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~ ~~ ~~~~~~~~ ~~~~~~~~ ~ ~~~ ~ ~~~~~~~~~~~~~~ ~ ~~ ~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~~ ~~~~ ~ ~~ ~~~ ~~ ~ ~ ~~~~~ ~~~~~ ~~~ ~~~~ ~ ~ ~~ ~ ~~~~~~~ ~ ~~ ~~ ~~~ ~~~~~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~ ~~~~~ ~~~~~~~~~~~~~~~~ ~~ ~~ ~~~~ ~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~ ~ ~~~~~ ~ ~~ ~~~~~~~~~ ~~~~~ ~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~ ~ ~~~~ ~ ~~~~~~~~ ~ ~~~~~~~ ~ ~ ~ ~ ~ ~~ ~~~~ ~~~~~ ~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~ ~~~~ ~~ ~~ ~~~ ~~~ ~~ ~~ ~~~ ~~~~~ ~~ ~~ ~~~ ~~~~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~ ~ ~ ~ ~ ~ ~~~~~~~ ~~~~ ~ ~~~~~ ~ ~ ~ ~~~~~~~~ ~ ~ ~ ~ ~ ~ ~~ ~~~ ~~~~~~~~~ ~ ~ ~~ ~ ~~ ~ ~ ~~~~~~~~~~~ ~ ~ ~~~~~~ ~ ~ ~~~ ~ ~~~~ ~ ~ ~ ~~ ~ ~ ~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~ ~~~ ~ ~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~ ~~ ~~~ ~~~~~~~~~~~~~~~~ ~~~~~~~~~ ~~ ~~ ~ ~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~ ~~ ~ ~ ~ ~~~~ ~~~~~~ ~~~ ~ ~ ~~ ~~ ~~~ ~~~~~ ~~~~~~~~~~~~~~~ ~ ~~ ~ ~~~~~ ~~~~~~~~~ ~~~~ ~ ~~~ ~ ~ ~ ~~~~~~~ ~ ~ ~ ~ ~ ~~ ~~ ~~~ ~~~~ ~ ~ ~~~~~~~~~ ~~ ~ ~ ~ ~ [...]... log I (y) } < e _,2 (7 5 7) But E(eyz ') < t 2