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- Consider the simple linear model Y, = Be + Bix, + C. where --N(0,a); i = 1,2, .., n. 1. Show that a) Y-IIN(B + B1*i,g²) b) (i) L = L(B.Pa:y) = (2ro) žexp - - Po + B,x,| (ü) a = (Sx - PSy) c) Cov(Be.B) = d) B, is an unhiased estimator of B, and that Var(B) = o 2. Derive the statisic for testing Ho: B - Bio versus H,: ß1 + Pin. (You must also state the distribution and critical region for the lest). 3. Constract a 100(1 – a)% confidence interval for 8,. %3D (Show all results used as part of your answer) %3DThe masses m, are located at the points P,. Find the moments M, and M, and the center of mass of the system. i' X, 2, m3 = 1, m4 = 4; m1 = 3, Pi(6, 3), Р.(3, -1), Р3(-2, 1), Рa(-2, -5) m2 Mx X, My = (х, у)Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a, b, c) = a) (2,1,-3) b) (2,-1,3) c) (-2,1,4) d) (2,-1,4) e) (2,0,0)
- The equations ry? + 6xzcos(u) + ye" = 12 and x³yz + xe" – 4u?v? = 12 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find ( ).y at P. %3D Türkçe: xy? + 6xzcos(u) + ye" = 12 ve æ³yz + xe" – 4u?v² = 12 denklemleri P noktası (ху2)-(1,1,1) ve (и, v) Çözümlü olsun. P'de ().y'yi hesaplayınız.) (4,0) civarında x,y ve z'nin fonksiyonu olmak üzere u ve v için du dz 11,y O 32,00 O -0,17 O 12,00 O -40,00 O - 30,00Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y = 2- x if 6(x, y) = (7)x + (5)y +C . %3DSuppose you are a bug buzzing around in space. You are currently at the point (1, 1, 0). If the temperature at point (x,y,z) is given by T(x, y, z) = xyz + x²y Z. If you are a bug that likes warm temperatures, which direction should you fly in to move in the direction of most rapid temperature increase? (0, 1, 2) (0, 2, 1) (1, 0, 2) ○ (1,2,0) (2,0,1) (2, 1,0)
- Find (x, y, z). (Let P = (7, 7, 0) and the Midpoint = (0, 5, 5).) %3D (х, у, 2) %3D ( Midpoint (х, у, 2)A golfer is videotaped and then has her swing displayed on a computer monitor so that it can be analyzed. Give the coordinates of the points that are highlighted in red. (Each block represents one unit.) (x, y) = ( (х, у) %3D ( (x, y) = ( ) (smallest x-value) ) ) (largest x-value)A particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point (1,2,3)to the point (5,4,1). Find the total work spent by the forces ?