21. (13; Assume that a two-dimensional random variable (X,Y) has the following joint probability distribution as X -2 0 4 -3 0.2 0.1 0.2 5 0.1 0.1 a (1) Find the value of a, (2) Find the marginal probability distributions of random variables X and Y, respectively, (3) Find the probability distribution of M = Min(X, Y), Y

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21. (15, Assume that a two-dimensional random variable (X,Y) has the following
joint probability distribution as
X
-2 0
4
-3
0.2
0.1
0.2
5
0.1 0.1
a
(1) Find the value of a,
(2) Find the marginal probability distributions of random variables X and Y,
respectively,
(3) Find the probability distribution of M = Min(X,Y),
(4) Are X and Y independent or not? Why?
(5) Calculate the expected value of X, that is E(X).
Y
Transcribed Image Text:21. (15, Assume that a two-dimensional random variable (X,Y) has the following joint probability distribution as X -2 0 4 -3 0.2 0.1 0.2 5 0.1 0.1 a (1) Find the value of a, (2) Find the marginal probability distributions of random variables X and Y, respectively, (3) Find the probability distribution of M = Min(X,Y), (4) Are X and Y independent or not? Why? (5) Calculate the expected value of X, that is E(X). Y
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