The joint pdf for rv X, Y is given as follows: if 1 ? x,y ?...

Question

Question

The joint pdf for rv X, Y is given as follows:

fx,y(x, y) = c(2²/y) if 1 ? x,y ? 2 and it is zero else.

Find:

(a) The value of c

(b) E(X)

(c) E(Y)

(d) E(X|Y)

(e) Var(X|Y)

(f) The MMSEE of e^X given Y , E(e^X|Y )

(g) Are X and Y independent?

math Statistics-And-Probability

Answer 1

Answer #1

=> Solution 、 - 乙 3 2 3 1 3 2 1-WL x? 3 3. in(%) DC -D 93 3 S 3 S 28 子 5. 1685 28 2 8 y are Independe

Answer 2

Similar Homework Help Questions

4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x <...

4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
Let (X,Y) have joint pdf given by f(rw)-y <x, 0 < x < 1, | 0,...

Let (X,Y) have joint pdf given by f(rw)-y <x, 0 < x < 1, | 0, 0.W., (a) Find the constant c. (b) Find fx (x) and fy(y) (c) For 0 < x < 1, find fy|x=r(y) and My X=r and oỉ x=x (d) Find Cov(X,Y). (e) Are X and Y independent? Explain why.
Let (X,Y) have joint pdf given by I c, \y < x, 0 < x <...

Let (X,Y) have joint pdf given by I c, \y < x, 0 < x < 1, f(x, y) = { | 0, 0.W., (a) Find the constant c. (b) Find fx(r) and fy(y) (c) For 0 < x < 1, find fy\X=z(y) and HY|X=r and oſ X=z- (d) Find Cov(X, Y). (e) Are X and Y independent? Explain why.

Let (X, Y) have joint pdf given by f(r, y)= < a, 0 < < 0,...

Let (X, Y) have joint pdf given by f(r, y)= < a, 0 < < 0, О.w., (a) Find the constant c (b) Find fx(x) and fy(y) (c) For 0 x< 1, find fyx=r (y) and py|x=x and oyx= (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
The joint pdf of X and Y is given by f(x, y) = C,0<x<y<1. a) Determine...

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.
3. (50 pts) Let (X, Y) have joint pdf given by c, y x, 0 <...

3. (50 pts) Let (X, Y) have joint pdf given by c, y x, 0 < x < 1, f(x, y) 0, o.w., (a) Find the constant c. (b) Find fx(x) and fy (y) (c) For 0 < 1, find fyx=x(y) and pyjx=x and oy Y|X=x (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why.

3. (50 pts) Let (X,Y) have joint pdf given by -{ c, lyl< x, 0 <...

3. (50 pts) Let (X,Y) have joint pdf given by -{ c, lyl< x, 0 < x < 1, f(x,y) = 0, 0.w., (a) Find the constant c. (b) Find fx(x) and fy(y) (c) For 0< x<1, find fy x-() and pyix- and ox (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 –...

0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 – x)y for 0 < x < 1, (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y. (d) Find Pſy < 81/2],P[X<Y]. (e) Are X and Y independent? (f) Find the correlation and covariance of X and Y. (g) Determine whether X and Y are uncorrelated. (h) Find fy(y|x) (i) Find E[Y|X = x]...
Given the joint pdf of the continuous RVs X and Y: fxy(x, y) = c for...

Given the joint pdf of the continuous RVs X and Y: fxy(x, y) = c for the region {0 sxs yo sy s 1} and zero elsewhere.Where “c” is a constant. Determine if the RV X and Y are independent.

Given the joint pdf of the continuous RVs X and Y: fxy(x, y) = c for...

Given the joint pdf of the continuous RVs X and Y: fxy(x, y) = c for the region {0 sxs y,0 < y < 1} and zero elsewhere.Where “c” is a constant. Determine if the RV X and Y are independent. (30 Marks)