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Homework Answers
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Please solve thank you. In Problem 27 of Exercises 4.9 you were asked to solve the...
Please solve thank you.
In Problem 27 of Exercises 4.9 you were asked to solve the following linear system dx1 1 dt 50 dx2 1 2 dt 50 75 dx3 1 2 x2 75 dt 25 using elimination techniques. This system is a mathematical model for the number of pounds of salt x(t), x2(t), and x3(t) in the connected mixing tanks A, B, and C shown in Figure 3.3.8 on page 112 (a) Use the eigenvalue method of this section...
(1 point) Let X1 and X2 be a random sample of size n= 2 from the...
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
Let X1, X2, ... be independent continuous random variables with a common distribution function F and...
Let X1, X2, ... be independent continuous random variables with a common distribution function F and density f. For k > 1, let Nk = min{n>k: Xn = kth largest of X1, ... , Xn} (a) Show Pr(Nx = n) = min-1),n>k. (b) Argue that fxx, (a) = f(x)+(a)k-( ++2)(F(x)* (c) Prove the following identity: al= (+*+ 2) (1 – a)', a € (0,1), # 22. i
2a) Let a, b e R with a < b and let g [a, bR be...
2a) Let a, b e R with a < b and let g [a, bR be continuous. Show that g(x) cos(nx) dx→ 0 n →oo. as Hint: Let ε > 0, By uniform continuity of g, there exists δ > 0 such that 2(b - a Choose points a = xo < x1 < . . . < Xm such that Irh-1-2k| < δ. Then we may write rb g (z) cos(nx) dx = An + Bn where 7m (g(x)...
I need help on part b, c, d, and f. Suppose X follows a N3( μ,...
I need help on part b, c, d, and f.
Suppose X follows a N3( μ, Σ ) distribution with 784 504-200 mean vector μ= | 130 | and covariance matrix 175 200 0 1600 a Find P(X, > 139). b Find p 12 Cor(X1. X2) c) Find P(X2> 139 |X1-103) "Hint": (Xi.X2) jointly follow a bivariate normal distribution d) Find P(X2< X e) Find P(X2<X3) Find P(X2〈 145〈X3) "Hint": P(X2〈145 & 145 〈 X 3) g)find P(X1 + 2X2+3X3>...
across Let F = (x i+yj +z k'). What is the outward flux of F (x2...
across Let F = (x i+yj +z k'). What is the outward flux of F (x2 + y2 +22)8 a sphere of radius R> 0 centered at the origin?
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) =...
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) = 2. o if 0<x< 1 else Find EY] where Y = min{X1, X2, X3, X4}.
(b) ONLY! Though you can use the result from (a) without proof (a) Let F(x) =...
(b) ONLY! Though you can use the result from (a) without
proof
(a) Let F(x) = x + x2 + x3 +... and let G(x) = x - x2 + x3 – x4.... Show that for k > 1 and n>k, (4")F(x)* = (n = 1) and if n < k then [x"]F(x)k = 0. (b) Show that G(F(x)) = x.
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
The Bessel equation of order one-half is X .2 dy d.2 + X dy dar +(x2...
The Bessel equation of order one-half is X .2 dy d.2 + X dy dar +(x2 - :) y = 0, X > 0 4 a) Verify that yı(x) = x-1/2 sin x is a solution to the equation b) Use reduction of order to find a second linearly independent solution. (Hint: one possibility is y2(x) = x-1/2 cos x.] c) Compute the Wronskian of these two solutions explicitly and verify that it is equal to the solution we computed...
Please solve thank you.
In Problem 27 of Exercises 4.9 you were asked to solve the following linear system dx1 1 dt 50 dx2 1 2 dt 50 75 dx3 1 2 x2 75 dt 25 using elimination techniques. This system is a mathematical model for the number of pounds of salt x(t), x2(t), and x3(t) in the connected mixing tanks A, B, and C shown in Figure 3.3.8 on page 112 (a) Use the eigenvalue method of this section...
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
Let X1, X2, ... be independent continuous random variables with a common distribution function F and density f. For k > 1, let Nk = min{n>k: Xn = kth largest of X1, ... , Xn} (a) Show Pr(Nx = n) = min-1),n>k. (b) Argue that fxx, (a) = f(x)+(a)k-( ++2)(F(x)* (c) Prove the following identity: al= (+*+ 2) (1 – a)', a € (0,1), # 22. i
2a) Let a, b e R with a < b and let g [a, bR be continuous. Show that g(x) cos(nx) dx→ 0 n →oo. as Hint: Let ε > 0, By uniform continuity of g, there exists δ > 0 such that 2(b - a Choose points a = xo < x1 < . . . < Xm such that Irh-1-2k| < δ. Then we may write rb g (z) cos(nx) dx = An + Bn where 7m (g(x)...
I need help on part b, c, d, and f.
Suppose X follows a N3( μ, Σ ) distribution with 784 504-200 mean vector μ= | 130 | and covariance matrix 175 200 0 1600 a Find P(X, > 139). b Find p 12 Cor(X1. X2) c) Find P(X2> 139 |X1-103) "Hint": (Xi.X2) jointly follow a bivariate normal distribution d) Find P(X2< X e) Find P(X2<X3) Find P(X2〈 145〈X3) "Hint": P(X2〈145 & 145 〈 X 3) g)find P(X1 + 2X2+3X3>...
across Let F = (x i+yj +z k'). What is the outward flux of F (x2 + y2 +22)8 a sphere of radius R> 0 centered at the origin?
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) = 2. o if 0<x< 1 else Find EY] where Y = min{X1, X2, X3, X4}.
(b) ONLY! Though you can use the result from (a) without
proof
(a) Let F(x) = x + x2 + x3 +... and let G(x) = x - x2 + x3 – x4.... Show that for k > 1 and n>k, (4")F(x)* = (n = 1) and if n < k then [x"]F(x)k = 0. (b) Show that G(F(x)) = x.
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
The Bessel equation of order one-half is X .2 dy d.2 + X dy dar +(x2 - :) y = 0, X > 0 4 a) Verify that yı(x) = x-1/2 sin x is a solution to the equation b) Use reduction of order to find a second linearly independent solution. (Hint: one possibility is y2(x) = x-1/2 cos x.] c) Compute the Wronskian of these two solutions explicitly and verify that it is equal to the solution we computed...
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