Probability

n.barsa
Posts: 4
Joined: Wed Sep 10, 2014 5:44 am

Probability

Postby n.barsa » Thu Mar 26, 2015 4:42 am

319.2. The following is a probability matrix for X = {1, 2, 3} and Y = {1, 2, 3}; i.e., the Joint
Prob (X = 3, Y = 3) = 18.0%:
Each of the following is true EXCEPT which is false?
a) X and Y are independent
b) The covariance(X,Y) is non-zero
c) The probability Y = 3 conditional on X = 1 is 10.0%; i.e., Prob (Y = 3, X = 1) = 10.0%
d) The unconditional probability that X = 2 is 50.0%; i.e., Prob (X = 2) = 50.0%

asamaha
Posts: 2
Joined: Thu Mar 26, 2015 8:28 am

Probability

Postby asamaha » Thu Mar 26, 2015 8:33 am

A

n.barsa
Posts: 4
Joined: Wed Sep 10, 2014 5:44 am

Probability

Postby n.barsa » Thu Mar 26, 2015 12:47 pm

Plz expalin . The answer given is

319.2. B. Because X and Y are independent, their covariance is zero (it is not true that we
can infer independence from zero covariance, however!).
In regard to (A), X and Y are independent because for all cells in the matrix: the Joint Prob
(X, Y) = Prob(X)*Prob(Y).
In regard to (C) and (D), these are TRUE.

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

Probability

Postby edupristine » Mon Mar 30, 2015 8:10 am

Hi, Since we can infer that X and Y are independent therefore covariance will be zero. When X and Y are independent covariance will be 0 but if covariance is 0 we cannot infer that X and Y are independent. Hence we can say that B will be false because covariance will be 0 and "not" non-zero.


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