State the properties of the distribution function.

1.	State the properties of the distribution function.
Answer» • Property 1: The distribution function F is increasing, (i.e) if x ≤ y, then F(x) ≤ F(y) • Property 2: F(x) is continuous from right, (i.e) for each x ∈ R, F (x⁺ ) = F (x) • Property 3: F (∞) = 1 • Property 4: F (-∞) = 0 • Property 5: F'(x) = f(x) • Property 6: P(a ≤ X ≤ b) = F(b) – F(a)

Answer»

• Property 1: The distribution function F is increasing, (i.e) if x ≤ y, then F(x) ≤ F(y)

• Property 2: F(x) is continuous from right, (i.e) for each x ∈ R, F (x⁺ ) = F (x)

• Property 3: F (∞) = 1

• Property 4: F (-∞) = 0

• Property 5: F'(x) = f(x)

• Property 6: P(a ≤ X ≤ b) = F(b) – F(a)

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