Re: Conceptual Doubts from Q 21-60-DSE 2011

Posted by Sinistral on May 29, 2013; 8:37am
URL: http://discussion-forum.276.s1.nabble.com/Conceptual-Doubts-from-Q-21-60-DSE-2011-tp7581391p7581443.html

"X and Y are given to have set intervals"??
what does this mean?

X can take either 1 or -1. and Y can take any integer in between [1,6]
respective probabilities of p(x,y) are given in that table (for various combinations of (x,y)   )

f_x(x) is marginal pmf of p(x,y)  --- (as it is the discrete case i am using p(x,y) instead of f(x,y). in f_x(x), f_x imples f subscript x. btw, to be more correct i shud have written it as p_x(x)  )

so p_x(x) (in my earlier hint i wrote it as f_x(x) ) can be found by summing all the values of p(x,y) for a given x. ie separately for x=1 and x=-1
so p_x(x) = .1 + a +.3 + 0 + 0 +0 for x=1
similarly one can find p_x(x) for x=-1

and obviously  p_y(y) is calculated in the same way
Please see that it can be done in that table itself. An extra column is appended for p_x(x) and an extra row is appended for p_y(y)

now p_x(x) & p_y(y) will satisfy al the properties of pdf (or pmf in this case). so, always greater than zero and summation over entire domain = 1.

For eg: p_x(x=1) + p_x(x=-1) =1
and so on.