A pair of random variables X and Y have continuous joint density function f(x,y) on (0,2)x(0,1) given by

f(x,y) = K(x^3 + xy) 0<x<2 , 0<y<1.

(a) Determine K

(b) Determine E[X]

(c) Determine V[X]

(d) Determine E[XY]

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- Jan 6th 2009, 08:54 AMmatty888Random Variables
A pair of random variables X and Y have continuous joint density function f(x,y) on (0,2)x(0,1) given by

f(x,y) = K(x^3 + xy) 0<x<2 , 0<y<1.

(a) Determine K

(b) Determine E[X]

(c) Determine V[X]

(d) Determine E[XY] - Jan 6th 2009, 09:12 AMmr fantastic
(a) Solve $\displaystyle \int_{x=0}^{2} \int_{y = 0}^1 f(x, y) \, dy \, dx = 1$ for K.

(b) Calculate $\displaystyle \int_{x=0}^{2} x \left( \int_{y = 0}^1 f(x, y) \, dy\right) \, dx$.

(c) Calculate $\displaystyle E(X^2) = \int_{x=0}^{2} x^2 \left( \int_{y = 0}^1 f(x, y) \, dy\right) \, dx$. Then $\displaystyle Var(X) = E(X^2) - [E(X)]^2$.

(d) Calculate $\displaystyle \int_{x=0}^{2} \int_{y = 0}^1 xy f(x, y) \, dy \, dx$. - Jan 6th 2009, 10:00 AMmatty888Thank you!!
Thanks a million mr. fantastic you are very helpful.

Could anyone confirm that my answers are right,not so sure myself(Wondering)

(a) K = 1/5

(b) 1.5466

(c) 3.741155

(d) 0.8177

Thanks(Happy) - Jan 7th 2009, 04:42 AMmr fantastic