Math Problem Statement
- A fun¸c˜ao densidade conjunta de X e Y ´e dado por fX,Y (x, y) = 1/2, −1 < x < 1, 0 < y < 1, 0, o.c. (a) X e Y s˜ao independentes?. Justifique; (b) Calcule P(X < Y ).
Solution
Dada a função densidade conjunta para e , que é definida como:
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Math Problem Analysis
Mathematical Concepts
Probability
Joint Density Function
Independence of Random Variables
Integration
Formulas
f_{X,Y}(x, y) = 1/2, -1 < x < 1, 0 < y < 1
f_X(x) = \int f_{X,Y}(x, y) dy
f_Y(y) = \int f_{X,Y}(x, y) dx
P(X < Y) = \int \int f_{X,Y}(x, y) dx dy
Theorems
Independence of random variables: f_{X,Y}(x, y) = f_X(x) f_Y(y)
Basic probability integration
Suitable Grade Level
Undergraduate
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