Joint Formula
Joint Formula
Are X and Y independent in this joint probability distribution table?
............y
-------0---1----2
x 0 0.2, 0.15, 0.05
....1 0.2, 0.25, 0
....2 0.10, 0.05, 0
The above table has commas where the column lines are meant to go, I have to work out of X and Y are independant and then justify it... but not sure what type of formula (or if that is how I do it) to use and how to justify it??? Can anyone point me in the right direction!? Thanks
get the sum of each row and column...
....... .......... ...... y
....... ..... 0 ....... 1 ....... 2
..... 0 .. 0.2 ... 0.15 ... 0.05 .... 0.4
x .. 1 .. 0.2 ... 0.25 ..... 0 ........ 0.45
..... 2 .. 0.1 ... 0.05 ..... 0 ....... 0.15
........... 0.5 ... 0.45 .... 0.05
note that
fx,y(0,1) = 0.15
but fx(0) * fy(1) = 0.4*0.45 = 0.18
thus X & Y are not independent... the above condition should work for all possible x and y.. . .
.. . .. .
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