If X and Y are independent and identically distributed exponential variables with parameter X = 4, compute each of the following joint densities. (a) U = 3X, V = 5X/Y. O= (a 'n)a'nf (b) U = 5X + Y,V = 3X/(X+Y). D= (a 'n)A'nf

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If \( X \) and \( Y \) are independent and identically distributed exponential variables with parameter \( \lambda = 4 \), compute each of the following joint densities.

(a) \( U = 3X, \, V = 5X Y \).  
\[ f_{U,V}(u, v) = \; \boxed{} \]

(b) \( U = 5X + Y, \, V = 3X/(X + Y) \).  
\[ f_{U,V}(u, v) = \; \boxed{} \]
Transcribed Image Text:If \( X \) and \( Y \) are independent and identically distributed exponential variables with parameter \( \lambda = 4 \), compute each of the following joint densities. (a) \( U = 3X, \, V = 5X Y \). \[ f_{U,V}(u, v) = \; \boxed{} \] (b) \( U = 5X + Y, \, V = 3X/(X + Y) \). \[ f_{U,V}(u, v) = \; \boxed{} \]
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