Thejoint PDFofabivariate RV (X,Y ) is given by fXY (x,y)= where k isaconstant. (a) Determine the...
Thejoint PDFofabivariate RV (X,Y ) is given by fXY (x,y)= where k isaconstant. (a) Determine the value of k. (b) Find themarginal PDFsof X andY. (c) Find P(0<X <1/2,0<Y <1/2). (d) Findtheconditional PDFs fY|X(y|x) and fX|Y (x|y). (e) Computetheconditional meansE[Y |x] andE[X|y]. (f) Computetheconditional variancesVar(Y |x) andVar(X|y). otherwise { k, 0<y≤x<1, 0, otherwise,
Thejoint PDFofabivariate RV (X,Y ) is given by fXY (x,y)= { k, 0<y≤x<1, 0, otherwise, where k isaconstant. (a) Determine the value of k. (b) Find themarginal PDFsof X andY. (c) Find P(0<X <1/2,0<Y <1/2). (d) Findtheconditional PDFs fY|X(y|x) and fX|Y (x|y). (e) Computetheconditional meansE[Y |x] andE[X|y]. (f) Computetheconditional variancesVar(Y |x) andVar(X|y).
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Thejoint PDFofabivariate RV (X,Y ) is given by fXY
(x,y)= where k isaconstant. (a) Determine the...
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded...
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded area Jxy(, 9) = 10 otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? b. Given the joint probability density function fxy(x, y) as, fxy(x, y) = { 0 kxy, (x, y) E shaded area otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? 2 1
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y)...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
Show all work! Thank you! Sk(x+y) 0<x<1, 0<y</ 14. Determine k, so that fx.y(x, y)= otherwise...
Show all work! Thank you!
Sk(x+y) 0<x<1, 0<y</ 14. Determine k, so that fx.y(x, y)= otherwise is a joint pdf. 10 15. Determine k, so that fxy(x,y)= kry 0<x<1, 0<y<1. 6 otherwise is a joint pdf. k(xy?) 0<x<1, 0<y<1. is a joint pdf. Determine k, so that fx.x(x,y)= 1 otherwise 17. Determine k, so that fx.y(x,y)= kr 0<x<y<1 O otherwise is a joint pdf. k(x + y) 0<x< y<1 18. Determine k, so that fx. (x,y)= 1 0 otherwise is...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
5. Let the joint density of X and Y be fr(x,) = (x + y, fxy(x, y) = 0, 0<x< 1,0 <y <1 otherwise (a) Find th...
5. Let the joint density of X and Y be fr(x,) = (x + y, fxy(x, y) = 0, 0<x< 1,0 <y <1 otherwise (a) Find the marginal pdfs of X and Y. (b) Are X and Y independent? (c) Are X and Y correlated? (d) Find P(X + Y < 1).
4. (14 pts) The joint pdf of X and Y is given by: (x + cya,...
4. (14 pts) The joint pdf of X and Y is given by: (x + cya, 0 SX S1,0 Sys1 fxy(x, y) = otherwise For this question, it may be useful draw the region in the X, Y plane where the pdf is non- zero to help you determine the limits of the integrals. (a) Find the value of the constant c. (b) Find the marginal pdfs of X and Y, respectively. (c) Find the probability that both X and...
MA2500/18 Section B (Answer THREE questions) 6. Let X and Y be jointly continuous random variables...
MA2500/18 Section B (Answer THREE questions) 6. Let X and Y be jointly continuous random variables defined on the same prob- ability space, let fx.y denote their joint PDF, and let fx and fy respectively denote their marginal PDFs (a) Let z be a fixed value such that fx(x) >0. Write down expressions for 12] (i) the conditional PDF of Y given X = z, and (i) the conditional expectation of Y given X (b) State and prove the law...
The joint pdf for rv X, Y is given as follows: if 1 ? x,y ?...
The joint pdf for rv X, Y is given as follows:
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 eX given Y , E(eX|Y )
(g) Are X and Y independent?
fx,y(x, y) = c(2²/y)
Let X and Y be continuous rvs with a joint pdf of the form: ?k(x+y), if(x,y)∈?0≤y≤x≤1?...
Let X and Y be continuous rvs with a joint pdf of the form: ?k(x+y), if(x,y)∈?0≤y≤x≤1? f(x,y) = 0, otherwise (a) Find k. (b) Find the joint CDF F (x, y). 0, otherwise (c) Find the conditional pdfs f(x|y) and f(y|x) (d) Find P[2Y > X] (e) Find P[Y + 2X > 1]
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given...
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given that X and Y are independent, their joint pdf is given by the product of the individual pdfs of X and Y, that is, fxy(x,y) = fx(x)fy(y) The joint pdf is defined over the same set of r-values and y-values that the individual pdfs were defined for. Using this information, calculate P(X - Y < t) where you can assume t is a positive...
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded area Jxy(, 9) = 10 otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? b. Given the joint probability density function fxy(x, y) as, fxy(x, y) = { 0 kxy, (x, y) E shaded area otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? 2 1
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
Show all work! Thank you!
Sk(x+y) 0<x<1, 0<y</ 14. Determine k, so that fx.y(x, y)= otherwise is a joint pdf. 10 15. Determine k, so that fxy(x,y)= kry 0<x<1, 0<y<1. 6 otherwise is a joint pdf. k(xy?) 0<x<1, 0<y<1. is a joint pdf. Determine k, so that fx.x(x,y)= 1 otherwise 17. Determine k, so that fx.y(x,y)= kr 0<x<y<1 O otherwise is a joint pdf. k(x + y) 0<x< y<1 18. Determine k, so that fx. (x,y)= 1 0 otherwise is...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
5. Let the joint density of X and Y be fr(x,) = (x + y, fxy(x, y) = 0, 0<x< 1,0 <y <1 otherwise (a) Find the marginal pdfs of X and Y. (b) Are X and Y independent? (c) Are X and Y correlated? (d) Find P(X + Y < 1).
4. (14 pts) The joint pdf of X and Y is given by: (x + cya, 0 SX S1,0 Sys1 fxy(x, y) = otherwise For this question, it may be useful draw the region in the X, Y plane where the pdf is non- zero to help you determine the limits of the integrals. (a) Find the value of the constant c. (b) Find the marginal pdfs of X and Y, respectively. (c) Find the probability that both X and...
MA2500/18 Section B (Answer THREE questions) 6. Let X and Y be jointly continuous random variables defined on the same prob- ability space, let fx.y denote their joint PDF, and let fx and fy respectively denote their marginal PDFs (a) Let z be a fixed value such that fx(x) >0. Write down expressions for 12] (i) the conditional PDF of Y given X = z, and (i) the conditional expectation of Y given X (b) State and prove the law...
The joint pdf for rv X, Y is given as follows:
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 eX given Y , E(eX|Y )
(g) Are X and Y independent?
fx,y(x, y) = c(2²/y)
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given that X and Y are independent, their joint pdf is given by the product of the individual pdfs of X and Y, that is, fxy(x,y) = fx(x)fy(y) The joint pdf is defined over the same set of r-values and y-values that the individual pdfs were defined for. Using this information, calculate P(X - Y < t) where you can assume t is a positive...
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