Dependent but Uncorrelated

xxxx xxxxxxxxxxx xx xxx xxxxxxxxxxxx. xxxxxxxx xxx xxxxxx xxxx, xxx xxx xxxxx xxx xxxxxxxxx xxx xxxxxxxxxxxxxx xx xxxxxx xx xxxxx xx xxxxxxx, xxxxx xx xxx xx xxxx xxxxx.

xxxxxxxxx xxxxxxxx_xxxxx(xxxxx).

xxxxx xx xxx xxxxxxx xx x xxxxx xxxxxxxxxxxx xxxx xxx xxxxxxx xxxxxxxxx, xxxxx xx (x, x, xxxxxx) xxxxxxx xxxx xxxxxxxx xxxxxxx xxxxxxx. xxxxxxxxxxxxx xxx xxx xxxxxxx xxxxxxx xx xxxxx xxxxx, xxx xxx xxxxxx xxxxx xxxx xx xxxxxxx xxxx xxxxxxxx. xxx (x, x) xxx xxxxxx xxx xxxxxx x.

xxxxxx (xxxxxxxxxxxx, xxxxxxxxxxx), xxxx xxxxxxxx:

• xxxxxxxxxxxx xxxxx ( xxxxxx{xxx}(x, x) = x ), xxxx xx ( x[xx] = x[x]x[x] );
• xxxxxxxxxxx xxxxx ( x(x = x, x = x) = x(x = x) x(x = x) ) xxx xxxxx xxxx, xxxxxxxxx xxx xxxxx xxxx xxxxxx x.

xx xxxxx xxxxxxx xxxxxxx (xxxx, xxxx).

xxxx xxxxx xxxx xx xxxxx. xxxxxxxx xxx xxxxx xxxxxx ( x ) xxxxx xxxx xxxx xxxxxxx xxxxxxxxxx:

[ x xxx x_x x_x x_x = xxxx(xxx x_x x_xxxxxx)xxxx(xxx x_x x_xxxxxx) ]

[ x(x, x) xxxx x = x_x(x) xxxx x_x(x) xxxx xxxx{xxx xxx } (x, x) ]

xxxxxxxx

xxxxxxxx_xxxxx([(-x, x, x), (x, x, x), (x, x, x)])
# (xxxx, xxxxx)

xxxxxxxx_xxxxx([(x, x, x), (x, x, x), (x, x, x), (x, x, x)])
# (xxxx, xxxx)

xxx xxxxx xx xxx xxxxxxx xxxxxxxxxxxxxx: ( x ) xxxxxxx xx ( {-x, x, x} ) xxx ( x = x^x ). xxxxxxxxxx xx xxxxxxx xxxx xxxxxxx ( x[x] = x ) xxx ( x[x^x] = x ) xx xxxxxxxx, xxx ( x ) xx x xxxxxxxx xx ( x ), xx xxxxxxx xxx xxxxx xxx xxx xxxxx xxxxxxx. xxxxxxxxxxx xxxxxxxx xxxxxx xxxxxxxxxxx xxxx, xxx xxxx xxxxxxxxxx xx xxxxxx xxxxxxxxx.

xxxxxxxxxxx

• x <= xxx(xxxxx) <= xx^x, xxxxxxx xxx xxxxxxxx, xxxxxx xxx xx xxx.
• xx (x, x) xxxx xx xxxxxx xxxxx.
• xxxxxxxxxxxx xxxx xxxx xxxx xxx xxxx xxxx xx xxxxxxxx ( x ) xxxxxx xxxxxxx xxxx xxxxxxxx ( x ) xxxxxx, xxx xxxxxx xxxx xxx xxxxxx xxxxx. x xxxx xxxxxxx xxxx xxx xxxxxxx xxx xxxxxxxxxxx x, xxx xxxxxxxxxxxx xxxxx xxxxxxx xxx xx xxx xxxxxxxxx xx xx x xxx, xxxxx xxxxxx xxxxxx xx xxxx xxxxxx xxx xxxxxxxx xxxxxxxxx.