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Question

5. For the joint PDF in Table 1

(a) sketch the PDF of X.

(b) sketch the CDF of Y.

(c) Are X and Y independent? Justify

(d) find the conditional PDF of Y given X = 1

(e) find the probability that Y is atleast 1, if X is equal to 1.

Table 1: Joint PDf for Question 5

I

0

1

2

0

0.12

0.08

0.06

Y

2

4

0.04

0.05

0.12 0.30

0.04

0.19

Fig: 1