11. Let X,Y are two continuous random variables with the following joint probability density function f(x,y)={4xy,0​0≤x≤

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11 Let X Y Are Two Continuous Random Variables With The Following Joint Probability Density Function F X Y 4xy 0 0 X 1 (17.07 KiB) Viewed 45 times

11 Let X Y Are Two Continuous Random Variables With The Following Joint Probability Density Function F X Y 4xy 0 0 X 2 (7.27 KiB) Viewed 45 times

11. Let X,Y are two continuous random variables with the following joint probability density function f(x,y)={4xy,0​0≤x≤1,0≤y≤1 otherwise ​. Find the expected value (E(X)) and the variance (Var(X)) of X. Hint: The expected value for random variable X is given by E(X)=∬R2​xf(x,y)dA E(X2)=∬R2​x2f(x,y)dAVar(X)=E(X2)−(E(X))2
12 Determine whether the following vector field is conservative. If it is conservative find f such that F=∇f. F(x,y)=(y2−2x)i+2xyj