Let the following be a joint probability mass function for t

Let the following be a joint probability mass function for the random variables X and Y.

a)Determine the marginal probability distribution of the random variables X and Y

b)Determine P(X1)

c) Determine P(Y<1.5)

d) Are the random variables X and Y independent? Why or why not?

e)Determine the conditional probability distribution of Y given that X= 1

f)Calculate the correlation coefficient between X and Y

f_xy(x,y)

1/8

1/4

1/2

a) To find pdf of x and y

Marginal density of x
x	0	1	2	Total
p	1/8	3/8	1/2	1
p*x	0	3/8	1	1 3/8
p*x^2	0	3/8	2	2 3/8
Variance				31/64

Marginal density of y
y	0	1	2	Total
p	1/8	3/8	1/2	1
p*y	0	3/8	1	1 3/8

b) P(X<=1)	1/2

c) P(Y<1.5)	1/2

d)	P(0,1) = 1/8
	P(X=0)P(Y=1)	3/64
	Since the two are not the same x,y are not independent.

e)	P(Y/x=1)
	y	0	1	2
	P(Y/x=1)	1/8	1/4	0