Let the random variable X and Y have joint pdf f(x,y)=4/7(x2 +3y2), 0<x<1, 0<y<1 a. find...
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Let
the random variable X and Y have joint pdf
f(x,y)=4/7(x2 +3y2), 0<x<1, 0<y<1
a. find...
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y...
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
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 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
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 <...
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
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.
4. Let X and Y be random variables of the continuous type having the joint pdf...
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
2. A continuous random variable has joint pdf f(x, y): xy 0 x 1, 0sys 2...
2. A continuous random variable has joint pdf f(x, y): xy 0 x 1, 0sys 2 f(x, y) otherwise 0 a) Find c b) Find P(X Y 1) b) Find fx(x) and fy(v) c) Are X and Y independent? Justify your answer d) Find Cov(X, Y) and Corr(X, Y) e) Find fxiy (xly) and fyixylx)
2. Let X and Y be continuous random variables having the joint pdf f(x,y) = 8xy,...
2. Let X and Y be continuous random variables having the joint pdf f(x,y) = 8xy, 0 <y<x<1. (a) Sketch the graph of the support of X and Y. (b) Find fi(2), the marginal pdf of X. (c) Find f(y), the marginal pdf of Y. () Compute jx, Hy, 0, 0, Cov(X,Y), and p.
Let X and Y be a random variable with joint PDF: f X Y ( x...
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
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.
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
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 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
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
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.
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
2. A continuous random variable has joint pdf f(x, y): xy 0 x 1, 0sys 2 f(x, y) otherwise 0 a) Find c b) Find P(X Y 1) b) Find fx(x) and fy(v) c) Are X and Y independent? Justify your answer d) Find Cov(X, Y) and Corr(X, Y) e) Find fxiy (xly) and fyixylx)
2. Let X and Y be continuous random variables having the joint pdf f(x,y) = 8xy, 0 <y<x<1. (a) Sketch the graph of the support of X and Y. (b) Find fi(2), the marginal pdf of X. (c) Find f(y), the marginal pdf of Y. () Compute jx, Hy, 0, 0, Cov(X,Y), and p.
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
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.
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