I am having trouble with part b.
Please explain. ![(2) Let Y be a linear function of X, ie. Y lo +biX where bo and bi are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the valucs of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is 2 Cov2(x,y) Hint: You may use the fact that Q(bg, bị) E [(Y-Y*)2-Var (Y-Y*) + IE(Y-Y*)]2 where Y* = bi + biX and bō, bị are the values you get from (a).](http://img.homeworklib.com/questions/1de1b560-72f6-11ea-886d-2dd0b74ca0ef.png?x-oss-process=image/resize,w_560)
Homework Answers
Here, we are concerned about the (b) part only. So I am not deriving the (a) part. Rather we are just using the results from part (a). First we will consider the sample of realizations of both X and Y variable and use them to get the b0 and b1. Then will prove the required by using the Hint.
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I am having trouble with part b.
Please explain.
(2) Let Y be a linear function...
(2) Let Y be a linear function of X, i.e. Y- bo biX where bo and...
(2) Let Y be a linear function of X, i.e. Y- bo biX where bo and bi are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity we=E[rMb, that minimize«Q (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ-ar 2 Cov2(x,Y) m Hint: You may use the fact that Q(bo,Y-YVar (Y -Y)+E (Y -Y)where Y.-bg + bİX...
(2) Let be a linear function of X, ie. = bo +b1X where bo and bi...
(2) Let be a linear function of X, ie. = bo +b1X where bo and bi are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ -c 3xy 2 Cov2 (X.y Hint: You may use the fat that (b,bE[(Y -Yar (Y - Y)E(Y - Y) where Y.-bg +...
Let Y be a linear function of X, i.e. Y = bo + bịX where bo...
Let Y be a linear function of X, i.e. Y = bo + bịX where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use(a) to show that the minimal value of Q is Co - Hint: You may use the fact that Q(bg, b) [(Y-Y*)2] = Var (Y-Y*) +E(Y-Y*)]2 where Y*-bg + bİX and bi,...
1. Let X and Y b e random variables, with μΧ = E(X), μΥ = E(Y),...
1. Let X and Y b e random variables, with μΧ = E(X), μΥ = E(Y), σ炙= Var(X) and σ Var(Y) (2) Let Ỹ be a linear function of X, ie. Ỹ = +51X where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ....
2. The linear regression model in matrix format is Y Χβ + e, with the usual definitions Let E(elX...
2. The linear regression model in matrix format is Y Χβ + e, with the usual definitions Let E(elX) 0 and T1 0 0 01 0 r2 00 0 0 0 0.0 0 γΝ 0 00 Notice that as a covariance matrix, Σ is bymmetric and nonnegative definite () Derive Var (0LS|x). (ii) Let B- CY be any other linear unbiased estimator where C' is an N x K function of X. Prove Var (BIX) 2 (X-x)-1 3. An oracle...
The Answer for i is suppose to be 0.625, but I am having trouble getting that...
The Answer for i is suppose to
be 0.625, but I am having trouble getting that number
Exercise 5.5. Consider the sample space S = {(x,y) € R2 : 22 + y2 <1}, with event space & suitably chosen, and with probability measure P determined by Area(E) Area(E) P(E) = Area(S) TT for E E E. Let X: S+R be the random variable defined by -1/2 if x < 0 and y 0, 1/3 if x < 0 and y...
I am having trouble with #2 X() xy = 1, y=0, x = 1, x =...
I am having trouble with #2
X() xy = 1, y=0, x = 1, x = 2, about 3 = -1. #2 Find the volume of the frustrum of a cone (i.e. the result of re- moving a smaller cone from the top of a larger cone) with height h, lower radius R and upper radius r. h R (Hint: Turn the cone on its side and draw a set of axes with the x axis piercing the centre of...
Assume b.1 is proven. Please help prove b.2 (b) Let f: V V be any linear...
Assume b.1 is proven. Please help prove b.2
(b) Let f: V V be any linear map of vector spaces over a field K. Recall that, for any polynomial p(X) = 0 ¢X€ K[X] and any vE v p(X) p(u) 2ef°(v). i-0 The kernel of p(X) is defined to be {v € V : p(X) - v = 0}. Ker(p(X)) (b.1) Show that Ker(p(X)) is a linear subspace of V. When p(X) = X - A where E K, explain...
I have solved the questions (a) to (c). Could you please help me with questions (d),(e),(f)? Thank you! 4. Suppose that(x,y), ,(XN,Yv) denotes a random sample. Let Si-a+bX, T, e+ dy, where a, b, c an...
I have solved the questions (a) to (c). Could you please help me
with questions (d),(e),(f)? Thank you!
4. Suppose that(x,y), ,(XN,Yv) denotes a random sample. Let Si-a+bX, T, e+ dy, where a, b, c and d are constants. Let X = Σ x, and with the analogous expressions for Y, S, T. Let ớXY = N- ρχ Y-σχ Y/(σχσΥ), with the analogous expressions for S, T. = NT Σ(X,-X)2, . Σ(X,-X)(X-Y), and let (a) Show that σ = b20%...
I am having trouble figuring out what should go in the place of "number" to make...
I am having trouble figuring out what should go in the place of "number" to make the loop stop as soon as they enter the value they put in for the "count" input. I am also having trouble nesting a do while loop into the original while loop (if that is even what I am supposed to do to get the program to keep going if the user wants to enter more numbers???) I have inserted the question below, as...
(2) Let Y be a linear function of X, i.e. Y- bo biX where bo and bi are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity we=E[rMb, that minimize«Q (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ-ar 2 Cov2(x,Y) m Hint: You may use the fact that Q(bo,Y-YVar (Y -Y)+E (Y -Y)where Y.-bg + bİX...
(2) Let be a linear function of X, ie. = bo +b1X where bo and bi are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ -c 3xy 2 Cov2 (X.y Hint: You may use the fat that (b,bE[(Y -Yar (Y - Y)E(Y - Y) where Y.-bg +...
Let Y be a linear function of X, i.e. Y = bo + bịX where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use(a) to show that the minimal value of Q is Co - Hint: You may use the fact that Q(bg, b) [(Y-Y*)2] = Var (Y-Y*) +E(Y-Y*)]2 where Y*-bg + bİX and bi,...
1. Let X and Y b e random variables, with μΧ = E(X), μΥ = E(Y), σ炙= Var(X) and σ Var(Y) (2) Let Ỹ be a linear function of X, ie. Ỹ = +51X where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ....
2. The linear regression model in matrix format is Y Χβ + e, with the usual definitions Let E(elX) 0 and T1 0 0 01 0 r2 00 0 0 0 0.0 0 γΝ 0 00 Notice that as a covariance matrix, Σ is bymmetric and nonnegative definite () Derive Var (0LS|x). (ii) Let B- CY be any other linear unbiased estimator where C' is an N x K function of X. Prove Var (BIX) 2 (X-x)-1 3. An oracle...
The Answer for i is suppose to
be 0.625, but I am having trouble getting that number
Exercise 5.5. Consider the sample space S = {(x,y) € R2 : 22 + y2 <1}, with event space & suitably chosen, and with probability measure P determined by Area(E) Area(E) P(E) = Area(S) TT for E E E. Let X: S+R be the random variable defined by -1/2 if x < 0 and y 0, 1/3 if x < 0 and y...
I am having trouble with #2
X() xy = 1, y=0, x = 1, x = 2, about 3 = -1. #2 Find the volume of the frustrum of a cone (i.e. the result of re- moving a smaller cone from the top of a larger cone) with height h, lower radius R and upper radius r. h R (Hint: Turn the cone on its side and draw a set of axes with the x axis piercing the centre of...
Assume b.1 is proven. Please help prove b.2
(b) Let f: V V be any linear map of vector spaces over a field K. Recall that, for any polynomial p(X) = 0 ¢X€ K[X] and any vE v p(X) p(u) 2ef°(v). i-0 The kernel of p(X) is defined to be {v € V : p(X) - v = 0}. Ker(p(X)) (b.1) Show that Ker(p(X)) is a linear subspace of V. When p(X) = X - A where E K, explain...
I have solved the questions (a) to (c). Could you please help me
with questions (d),(e),(f)? Thank you!
4. Suppose that(x,y), ,(XN,Yv) denotes a random sample. Let Si-a+bX, T, e+ dy, where a, b, c and d are constants. Let X = Σ x, and with the analogous expressions for Y, S, T. Let ớXY = N- ρχ Y-σχ Y/(σχσΥ), with the analogous expressions for S, T. = NT Σ(X,-X)2, . Σ(X,-X)(X-Y), and let (a) Show that σ = b20%...
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