Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

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.

Expert Solution

Colby Messinger answered 2 years ago

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y...

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y <= 1, 2*y <= x. (And 0 otherwise) Let the random variable W = X + Y. Without knowing the p.d.f of W, what interval of w values holds at least 60% of the probability?

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1,...

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...

G1. Let f(x, y) = 1 for 0 < x < 1 and x < y...

G1. Let f(x, y) = 1 for 0 < x < 1 and x < y < (x + 1); and 0 otherwise. Find the correlation coefficient for this X and Y . (Hint: the answer is p (1/2) = 0.7071. See if you know all of the steps needed to get there.)

Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)

f(x,y)=30(1-y)^2xe^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta...

f(x,y)=30(1-y)^2*x*e^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta random variable with parameters alfa=3 and Beta=3. b). show that f(x|y) the conditional density function of X given Y=y is a Gamma random variable with parameters alfa=2 and beta=y. c). set up how would you find P(1<X<3|Y=.5). you do not have to do any calculations

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does...

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does not equal to 0 3. f'(0)=1 Then: a) Show that f(0)=1. (Hint: use the fact that 0+0=0) b) Show that f(x) does not equal to 0 for all x. (Hint: use y= -x with conditions (1) and (2) above.) c) Use the definition of the derivative to show that f'(x)=f(x) for all real numbers x d) let g(x) satisfy properties (1)-(3) above and let...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value of k that makes this a probability density function. Compute the probability that P(X≤3/4, Y≥1/2). Find E(X). Find E(X|Y=y).

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is...

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is a joint pdf. b. Find the correlation coefficient of X and Y.

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation...

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation coefficient ρX,Y . 5. The height of female students in KU follows a normal distribution with mean 165.3 cm and s.d. 7.3cm. The height of male students in KU follows a normal distribution with mean 175.2 cm and s.d. 9.2cm. What is the probability that a random female student is taller than a male student in KU?

Let f (x, y) = c, 0 ≤ y ≤ 4, y ≤ x ≤ y...

Let f (x, y) = c, 0 ≤ y ≤ 4, y ≤ x ≤ y + 1, be the joint pdf of X and Y. (a) (3 pts) Find c and sketch the region for which f (x, y) > 0. (b) (3 pts) Find fX(x), the marginal pdf of X. (c) (3 pts) Find fY(y), the marginal pdf of Y. (d) (3 pts) Find P(X ≤ 3 − Y). (e) (4 pts) E(X) and Var(X). (f) (4 pts) E(Y)...

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