Double Integrals by Summing Values of a Cumulative Distribution Function
Double Integrals by Summing Values of a Cumulative Distribution Function
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Let be a function, and suppose that its "cumulative distribution function" , is known. is the integral of over the rectangle below and to the left of , and the double integral of over a rectangle can be computed easily in terms of the values of at the corners via:
f
F(x,y)=f(u,v)dudv
y
∫
u=0
x
∫
v=0
F(P)
f
P
f
F
∫∫
ABCD
Checking boxes causes a region to be shaded such that the combination values at the checked corners is the integral of over the shaded region.
F
f