45 Joint Gaussian Probability Density Function The joint Gaussi... | Filo

SOLVED:Probability A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties. (a) f(x, y) ≥0 for all (x, y) (b) ∫-∞^∞ ∫-∞^∞ f(x, y) d A=1 (c) P[(x, y) ∈R]=∫R ∫f(x, y) d A Show that the function is a joint density function and find the required probability. f(x, y)={ (1)/(27)(9-x-y), 0 ≤ x ≤ 3,3 ≤ y ≤ 6 0, elsewhere . P(0 ≤ x ≤ 1,4 ≤ y ≤ 6)

Probability Density Function | Formula, Properties & Examples