Notes
1. Cov of Yo with anything is 0, as Yo is fixed. As well as V(Yo)=0.
2. Cov of any Epsilon with itself(irrespective or time period) is 0, because they are i.i.d's.
3. Var(a+b) = v(a) + v(b) + 2cov(a,b)
id 3. Suppose Y, = Y,_,+,, ę, ~ (0,0²). Show that cov[Y,,Y,+h] = to’, and dividing...
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
2. Suppose the variables Yi and Y have the following properties EQİ)-4, Var(h)-19, E(Y )-6.5, Var(Ya)-5.25, E(Y3%)-30 Calculate the following; please show the underlying work a) (3 pts) Cov(, ) b) (3 pts) Cov(41, 3%) c) (3 pts) Cov(41.5-½) (6 pts) Find the correlation coefficient between 1 + 3, and 3-2%
can you help with these questions and briefly explain
how you got to the answer. it would be a big help thank for your
time.
Question 1 Suppose that the conditional variance is var(WXi) = (x), where i is a constant and h is a known function. The WLS estimator: O A. is the estimator obtained by first dividing the dependent variable and regressor by h and then regressing this modified dependent variable on the modified regressor using OLS. O...
2,t31. Find the li y-In | 4y+TI. Find the linearization of h at (z,y) = (0,0). 2. Leth(z 3. Let H(z,y)-z' + ya_ 4zy + 2 on the domain DH = { (zw) e R2 l o 2). Find all local and 4,0 y absolute extrema of H on DH ANSWERS
2,t31. Find the li y-In | 4y+TI. Find the linearization of h at (z,y) = (0,0). 2. Leth(z 3. Let H(z,y)-z' + ya_ 4zy + 2 on the domain...
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B Find functions g and h such that X, has the same covariance as a Brownian bridge.
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B...
4. (12 pts) Suppose that (Y, X:) satisfy the three assumptions we made in the regression analysis, and in addition, u; is N(0,0%) and is independent of Xi. A random sample of size n = 32 is drawn and yields Y = 43.2 + 61.5 x X, R' = 0.54, SER= 1.52 (10.2) (7.4) where the numbers in parentheses are the homoskedastic-only standard errors for the regression coefficients. (i) Construct a 99% confidence interval for 3. (ii) Test H, :...
Suppose X, Y and Z are three different random variables. Let X obey Bernoulli Distribution. The probability distribution function is p(x) = Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y ∼ N(0, 1). X and Y are independent. Meanwhile, let Z = XY . (a) What is the Expectation (mean value) of X? (b) Are Y and Z independent? (Just clarify, do not need to prove) (c) Show that Z is also a standard...
Problem 3 (12 points): Let D be a bounded domain in R" with smooth boundary. Suppose that K(x, y) is a Green's function for the Neumann . For each x E D, the function y H K(x, y) is a smooth harmonic For each x E D, the normal derivative of the function y K(x, y) . For each z e D, the function y K(x,y)-Г(z-y) is smooth near problem. This means the following: function on D(r satisfies (VyK(x, y).v(b))-arefor...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show at eq. point (4,0) the Jacobian matrix is -4 -8 0 1 f) draw phase portrait near (4,0) from (d) g) at eq. point (2,1) the Jacobian matrix is -2 -4 0.5 0 h) draw phase portrait near (2,1) from (f) i)...
please show work and answer 12,13,14,15
Question 12:11 point) **(*)-. And y) (3) () 30 0 120 c) 60 (420 72 Question 13:11 point Find the interval on which f(x)-1 s increasing () (- . 1] (d) (- *. 3] (*) (-, 2] Question 14: (1 point) Find or slope of the tangent link to the curvoy- t at the point ( 1 ) a) 14 144 c) -12 02 (e)-1 Question 15: point Penang through the origin (0,0). There...