prob 5 Random variables X and Y have joint PDF given by 10 S

prob

5\') Random variables X and Y have joint PDF given by 1,0 S y fx, r, y) otherwise Determine the expected value Elx Yl. Determine the expected values Elxland E[Y]. Let A ty s r). Determine P A

Solution

E[X+Y] =integral(0->1)integral(0->1) (x+y)3y dxdy

=integral(0->1)integral(0->1) (xy+3y^2) dxdy

=integral(0->1) (0->1) (xy^2/2+y^3) dx

=integral(0->1) (x/2+1) dx

= (0->1) x^2/4 +x

= 1/4 +1

= 5/4 Answer

E[X] =integral(0->1)integral(0->1) (x)3y dxdy

=integral(0->1)integral(0->1) (3xy) dxdy

=integral(0->1) (0->1) (3xy^2/2) dx

=integral(0->1) (3x/2) dx

= (0->1) 3x^2/4

= 3/4 Answer

E[Y] =integral(0->1)integral(0->1) (y)3y dxdy

=integral(0->1)integral(0->1) (3y^2) dxdy

=integral(0->1) (0->1) (y^3) dx

=integral(0->1) (1) dx

= (0->1) x

= 1 Answer

P(A) =integral(0->1)integral(0->x) 3y dxdy

=integral(0->1)integral(0->x) (3y^2) dxdy

=integral(0->1) (0->x) (y^3) dx

=integral(0->1) (x^3) dx

= (0->1) x^4/4

= 1/4 Answer

= 5/4 Answer