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(Solved): Two discrete random variables \( X, Y \) follow a distribution with joint function probability mas ...
![Two discrete random variables \( X, Y \) follow a distribution with joint function probability mass
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f(x, y)=P[X=x, Y=y]=\f](https://media.cheggcdn.com/media/553/553776dc-c99e-4051-89fa-28db08b774f8/phpYRC6jG)
Two discrete random variables \( X, Y \) follow a distribution with joint function probability mass \[ f(x, y)=P[X=x, Y=y]=\frac{c}{2^{x} \cdot 4^{y}} \] for some suitable real constant \( c \). (a) Find the value of the constant \( c \). (b) Find the marginal probability mass functions of \( X, Y \). (c) Calculate the following probabilities \[ \begin{array}{l} P(X+Y=2) \text { and } \\ P(X+Y>2 \mid Y<2) . \end{array} \]
Expert Answer
Solution:- The joint pmf of X and Y is f(x,y)=c2x.4y?if?x=0,1,2,….;y=0,1,2,…. = 0 ot