Let X and Y be two continuous random variables with joint probability density f(x, y) The joint distribution function F(a, b) is defined as follows Verify each of the following a F ( , ) F( , y) F(x, ) 0 b F (, ) 1 c If a 2 a 1 and b 2 b 1 ,then F (a 2 , b 2 ) F (a 1 , b 2 ) F (a 2 , b 1 ) F (a 1 , b 1 ) F(a, b) P(X s a, Y s b) f(x, y) dy dx 3D

Question: Let X and Y be two continuous random variables with joint probability density f(x, y). The joint distribution function F(a, b) is defined as follows:

Let X and Y be two continuous random variables with joint probability density f(x, y). The joint distribution function F(a, b) is defined as follows:

F(a, b) = P(X s a, Y s b) = f(x, y)

Verify each of the following:

a. F (-∞, -∞) = F(-∞, y) = F(x, -∞) = 0

b. F (∞, ∞) = 1

c. If a₂≥ a₁ and b₂ ≥ b₁ ,then F (a₂, b₂) - F (a₁, b₂) ≥ F (a₂, b₁) - F (a₁, b₁).

F(a, b) = P(X s a, Y s b) = f(x, y) dy dx %3D

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