Two continuous random variables X and Y have the following bivariate probability function which is defined over the unit square: fxy(x,y) = (9 - 6x - 6y + 4xy)/4 0≤x,y≤1, 0 Otherwise a. Given that R is the unit square, verify that: ∫∫fXY(x,y)dxdy=1 b. Determine fX(x) and fY(y). c. Hence state whether or not the two random variables are independent.
Two continuous random variables X and Y have the following bivariate probability function which is defined over the unit square: fxy(x,y) = (9 - 6x - 6y + 4xy)/4 0≤x,y≤1, 0 Otherwise a. Given that R is the unit square, verify that: ∫∫fXY(x,y)dxdy=1 b. Determine fX(x) and fY(y). c. Hence state whether or not the two random variables are independent.
Two continuous random variables X and Y have the following bivariate probability function which is defined over the unit square: fxy(x,y) = (9 - 6x - 6y + 4xy)/4 0≤x,y≤1, 0 Otherwise a. Given that R is the unit square, verify that: ∫∫fXY(x,y)dxdy=1 b. Determine fX(x) and fY(y). c. Hence state whether or not the two random variables are independent.
a. Given that R is the unit square, verify that: ∫∫fXY(x,y)dxdy=1
b. Determine fX(x) and fY(y).
c. Hence state whether or not the two random variables are independent.
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1. Two continuous random variables X and Y have the following bivariate probability
function which is defined over the unit square:
f xv(x, y)
бх
бу + 4ху)/4
0 < x, y < 1
therewise
a. Given that R is the unit square, verify that
|| fxv(x, y) dx dy = 1.
b. Determine fx(x) and fr(y).
c. Hence state whether or not the two random variables are independent.
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19/04/2021
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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