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

x

y

f_xy(x,y)

0

1

1/8

1

0

1/8

1

1

1/4

2

2

1/2

Solution

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

c) P(Y<1.5) = 1/2

e) P(Y/x=1)

is y        0     1     2

   p         1/8 1/4 0

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f) E(XY) = sum of xyP(XY)

= 1/4 + 4(1/2)

= 9/4

E(X)E(Y) = (3/2)(3/2) = 9/4

Hence cov (xy) =0

Corre = 0