Suppose (X,Y)∼Unif(A), whereA⊆R2 is the triangular region connecting vertices (0,2),(2,0), and (2,2). FindCor(X,Y).
Suppose (X,Y)∼Unif(A), whereA⊆R2 is the triangular region connecting vertices (0,2),(2,0), and (2,2). FindCor(X,Y).
Verify Green's theorem for the triangular region with the vertices (0,0), (1,2), and (0,2) and the vector field F(x,y) = 2y2i + (x + 2y)?j.
10. Consider the triangular region R with vertices (0.0) (a) (4 points) Sketch the triangular region R. Vertices (0.0), (0,2), and (4,0) 3/ lebel up, but do not evaluate, an integral for the volume of the solid obtained by rotating the triangular region R abo al (c) (4 points) Set up, but do not evaluate, an integral for the volume of the described solid. The base is the triangular region R. The cross-sections perpendicular to the r-axis are semi-circles with...
3. The pair of random variables X and Y is uniformly distributed on the interior of the triangle with the vertices whose coordinates are (0,0), (0,2), and (2,0) (i.e., the joint density is equal to a constant inside the triangle and zero outside). (a) (10 points) Find P(Y+X< 1). (b) (10 points) Find P(X = Y). (c) (10 points) Find P(Y > 1X = 1/2).
3. The pair of random variables X and Y is uniformly distributed on the interior...
Integrate f(x,y)=x2 + y over the triangular region with vertices (0,0), (1,0), and (0,1). The value is (Type a simplified fraction.)
find Ssey R R is a triangular region in x-y plane with vertices (-2, 2), (0,0), (2, 2)
Find the volume under the graph of the function f(x,y)=10x^2y . A triangular region with vertices (2,6), (6,6), and (6,18).
(15 pts) Find (2x - y) dA, where R is the triangular region with vertices (0,0), (1, 1), and (2, -1). Use the change of variables u = x - y and v = x + 2y.
Q3. If R is the triangle with vertices (2,0), (6,4) and (1,4), then draw the region R' after applying the transformation x = (u – v), y =(u + 40). Also, write the limit for integration in both region, i.e. Ne f(x,y) dA = write the limit for x,y and then covert the integration with limit in R' ?
sin()ddy, where the boundary of R is the trapezoid 2. Evaluate with vertices (1,1), (2,2), (4,0), (2,0). Use change of variables u y-x, vy+x.
sin()ddy, where the boundary of R is the trapezoid 2. Evaluate with vertices (1,1), (2,2), (4,0), (2,0). Use change of variables u y-x, vy+x.
(b) Evaluate the double integral e(y-2)/(y+2) dA where D is the triangle with vertices (0,0), (2,0) and (0,2). (Hint: Change variables, let u = y - x and v = y + x.)