Question

1. (6 marks) The joint probability mass function of X and Y is given by the following table.

  

f (x,y)		x
		-1	2
y	0	5/18	1/9
	1	2/9	q
	3	5/27	1/6

(a) Find the value of q such that the table given above is a valid joint probability mass function.

(b) Find the marginal probability mass function of Y .

(c) Calculate the following three probabilities:

• P ((X − 2)^2 = 0)

• P (Y < 2 )

P(Y = 3 | X = 2)

(d) Are the two random variables X and Y independent? Prove your answer

Answer 1