The joint PDF of X and Y is given by f(x, y) = C, (0<
x<y<1).
a) Determine the value of C
b) Determine the marginal distribution of X and compute E(X) and
Var(X)
c) Determine the marginal distribution of Y and compute E(Y) and
Var(Y)
d) Compute the correlation coefficient between X and Y
1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1, zero
elsewhere, be the joint probability density function(pdf) of X and
Y . Find P(0 < X < 1/2 , 1/4 < Y < 1) , P(X = Y ), and
P(X < Y ). Notice that P(X = Y ) would be the volume under the
surface f(x, y) = 4xy and above the line segment 0 < x = y <
1...
Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,
f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the
Lagrange interpolation F(x, y) that interpolates the above data.
Use Lagrangian bi-variate interpolation to solve this and also show
the working steps.