Answer to Question #46250 in Statistics and Probability for Divyashree Bhat

Question

The joint probability function of two discrete random variables X and Y is given by
f(x
,y) = c(2x+y)
, where
x
and
y
can assume all integral values such that
0
≤
x
≤
2,
0
≤
y
≤
3
, and
f(x, y) = 0
otherwise. Find the value of th
e constant
c
,
(ii) P(x=2,
y=1), (iii) P(x≥1, y≤2)
, (iv) Marginal probability functions of X and Y. Check
whether X and Y are independent