Let the joint probability density function of two-dimensional random variables (x, y) be: F (x, y) = {2; 0 < y < x < 10; others (1) Finding the edge density functions FX (x) and FY (y) of X and Y (2) Ask if x and y are independent of each other

Let the joint probability density function of two-dimensional random variables (x, y) be: F (x, y) = {2; 0 < y < x < 10; others (1) Finding the edge density functions FX (x) and FY (y) of X and Y (2) Ask if x and y are independent of each other

The density function should not be capitalized as much as possible, which is generally used to represent the distribution function
fx(x)=∫(0~x) 2 dy
=2x
fy(y)=∫(y~1) 2 dx
=2(1-y)
x. Y is not independent of each other
Because FX (x) FY (y) = 4x (1-y) is not equal to f (x, y)