Ex 1.4: Suppose n observations X1, X2,..., Xn have mean μ, variance σ², and cor(Xi, Xi+1) = p for all i. All other correlations equal zero. (a) If show that X = n n Σχε var (X) = (1 + n 2(n−1)p). (b) Deduce that if p > 0 the confidence interval for μ will be wider than in the case with {X+} independent. What happens if p < 0? Hints: (1) Recall that n n var(X) = ΣΣ cov(Xi, Xj). i=1 j=1 How many terms have i = j? How many have i - j = ±1? (2) Recall that cov(Xi, X;) = cor(Xi, X;)√/var(X;) var(X;).
Q: Please solve Linear Algebra and show all steps. Thank you.
A: Step 1:
Q: (6) Determine the applied force P required to keep the 200 kg engine in the equilibrium position for…
A: Given mass of engine (m) = 200 kgSo, the weight of the engine (W) = m*gHere, g is the acceleration…
Q: Determine the magnitude and coordinate direction angles of the resultant force of the three given…
A:
Q: Explain each step, simple and organize solution
A:
Q: not use ai please
A: The second derivative test f"(x) tells us about the concavity at x.f" > 0 or positive then f is…
Q: Exercise 4o | Describe Ken T, where T: IR" - IR³ is given by the matrix A = 114 71 25 81 36 91
A: Step 1:Step 2: Step 3: Step 4:
Q: 12. Solve the following recurrence relations by the method of generating functions.
A:
Q: What is the inverse Laplace Transform for the function F(s) if one term is 1/(s+a), another is…
A:
Q: כ Q3. What is the relationship between Laplace transform == .co L[u(t)] = F(s) est u(t)ȧt and the…
A: Q3: Relationship between Laplace Transform and the Given Transform The given transform:…
Q: Don't use chat gpt
A: (a) Identify which of the points in the table are critical points.A critical point occurs when the…
Q: A difference in elevation between A and B was observed four times as 44.07, 44.03, 44.11, and 44.01…
A:
Q: "" Shove that if hez) is a complex -valued harmonic function Csolution of Laplace's equation) such…
A:
Q: Don't use chat gpt It Chatgpt means downvote
A: Let's go step by step to solve the problem manually, using the principles of Fourier series…
Q: (2) A person exerts a force P = 6 lb to open the door as shown. The applied force P lies in the…
A:
Q: Tailwind, Inc., produces high-quality but expensive training shoes for runners. The Tailwind shoe,…
A: Cycle time Explanation: Cycle time is the available average time for completing each unit of item.…
Q: The hoisting drum of diameter d = 20 cm rotates with a constant angular velocity of 4 rad/s and…
A: Answer:
Q: Set theory
A: Let me know if you'd like further clarification on any part of these proofs!
Q: AP 5m long and 3.5 m wide is dark to a certain debt if the volume of earth taken out of it is 14 m…
A: We have given, Length of pit (L) =5 meterWidth (W) =3.5 meterLet depth of pit (D) = h meterVolume of…
Q: Don't use chat gpt
A:
Q: Solve the following Gourset problem Utt - Uxx Uxx = 0 U|x-t=0 = 4x² U|x+t=0 = 4x.
A:
Q: If TR2 R2 is a linear transformation such that →> 13 6 48 = (A)-G]([3])-4)] T = and T 37 then the…
A:
Q: Im focused on figuring out how to do the second problem
A: I hope you find this helpful. If you have any question or clarification, do not hesitate to reach…
Q: Evaluate the integral using Cauchy theorem, where the a and b are inside the contour. Please show…
A: We evaluate the integralI=∫C(z−a)(z−b)1dz by using Cauchy's theorem, where C is a closed contour…
Q: can you show me the easiest way to solve these ode's Solve (3x^2 + y) dx + (x + 3y^2) dy = 0. Solve…
A:
Q: Exercise 3. Sketch the following subsets of C, and say which of them are open in C and closed in C.…
A: Set A = {z ∈ C : 1 < |z| < 3, Im(z) ≥ 0} Step 1: Understand the components z is a complex…
Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…
A: Step 1: We'll perform row operations on A to reduce it to the identity matrix. Each row operation…
Q: A pharmacist had previously prepared a stock solution at a 150 mg/mL concentration. What volume of…
A: It is possible to find the volume of concentrated solution used to make dilute solution using the…
Q: Find all separated solutions for the following PDEs using the separation ansatz u(x,y) = X(x)Y(y)…
A:
Q: The equations have to look like the 2 pictures
A: Step 1: Step 2:Step 3: Step 4:
Q: Let S be the part of the plane 2x + 3y + z = 3 which lies in the first octant, oriented upward. Find…
A: To find the flux of the vector field F = i + 2j + 3k across the surface S (the part of the plane 2x…
Q: A 60-kg woman holds a 9-kg package as she stands within an elevator which briefly accelerates…
A:
Q: (1) Two cables AB and AC are attached to the tower. If the tension in cable AB is T₁ = 8 kN and the…
A:
Q: Change 101975 inches to miles (round to 3 sig figs)?
A: Before we start the conversion, we need to understand the conversion factors. There are 12 inches in…
Q: Example Find equations of the tangent and the normal at a point A = (6,4) to the curve A = (6,4) 2 0…
A: We find the equations of the tangent and normal lines at the point A = (6, 4) on the curve defined…
Q: Discrete Mathmatics
A: Step 1: Step 2: Step 3: Step 4:
Q: What does 710 and 213 mean? Please explain. Thank you.
A: 710 is a notation that represents the number 7 in base 10.In number systems, the subscript denotes…
Q: Pls help ASAP, and pls show all work and steps and circle the final answer.
A: Step 1:Step 2: Answer: (a) 1/3 (b) 1/3 (c) -3
Q: Pls help ASAP, and show all work and steps and please circle the final answer.
A: Given Function:The original function is y=log2(x), which represents the logarithm base 2 of x. Step…
Q: Compute the matrix P that performs a change of basis from basis B to basis C of R3 below, where the…
A: .
Q: (6) The tension force in cable AB is T = 40 kN acting on the crane as shown. Use vector cross…
A: Approach to solving the question: Detailed explanation:Examples: Key references:
Q: Please andwer
A: This image is a logic puzzle. Let's analyze each statement and determine whether it is true (T) or…
Q: Don't use chat gpt It
A: a. Eigenvalues and EigenvectorsTo find the eigenvalues, we need to solve the characteristic…
Q: (4) Determine the angle between the 200 lb force F and line OC. Ans: 54.9° + 24" B F = 200 lb 8" y…
A: Step 1: Step 2: Step 3: Step 4:
Q: Solve by using RREF method.
A: #1. Solve the system:x + 3y = 9 2x + y = 8Step 1: Set up the augmented matrixAn augmented matrix…
Q: Suppose lim xf(x) = L, where LE R. Prove: lim 8+← 8+个8 f(x) = 0.
A: Given :limx→+∞xf(x)=L,L∈Rand we need to prove:limx→+∞f(x)=0.Conclusion:Therefore, in both cases,…
Q: Please solve and show all steps.
A: Step 1: Write the associated matrix.The associated matrix with respect to the given vector would…
Q: Show that an edge e is a bridge of a graph G if and only if {e} is a bond of G.
A: We prove that an edge e is a bridge of a graph G if and only if {e} is a bond of G. We need to…
Q: Find the equilibrium solutions and analyze the stability using the phase diagram.
A: Step 1:Step 2:
Q: Linear AlgebraShow calculations
A: Step 1: Step 2: Step 3: Step 4:
Q: Linear Algebra show calculations
A: Let's assume that the vectors u + v, u - v, u - 2v + w are linearly dependent. This means that there…
Step by step
Solved in 2 steps
- Q3. Let Xj and X, be independent observations from a distribution with mean e and variance o7. Consider the following two estimators for 0: Ô =X, and Ô, =(2X,+X2)/3. (a) Show that Ô, and Ô, are both unbiased estimators of e. (b) Obtain the relative efficiency of 6j to ê2. (c) Which estimator, 6, or O, is a more efficient estimator? Justify your answer.6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1Answer the following questions with TRUE or FALSE, and explain your answer: (a) Let a random sample of independent X1 , . . . Xn be taken from a population with mean µx , variance σ2x . Then, the variance of X bar, (the sample mean) will always be less than or equal to the variance of X. (b) If X and Y have correlation 0.50, then the correlation between 4X and 5Y will not be 0.50. (c) For n dependent random variables X1 , . . . , Xn , drawn from the same population with mean µx ,E[X bar] = µx . (d) If X has a variance of 4 and mean of 2, and a sample mean based on 4 independent Xi wascalculated, the probability that X will be larger than 8 is larger than the probability that X bar islarger than 8. ***Note: (Please do not copy answer from Chegg!)
- 3. Let X N(u,0²). Find the MSE of the (uncorrected) sample variance 152 as an estimator for ² and compare with the MSE of the (corrected) sample variance S².4. If x' and y' are the deviations of the variables X and Y from their means, s, s are the variances of variables X and Y, correlation coefficient between variables X and Y is r and (X, Y) for i = 1, 2, n are the n values of (X, Y), then show that Hence prowa x x $2 $1 =1-12/12/2012 2n ...9 100 =−1+ Xi Xi + 2n 2n=1 $1. $₂ balles ad no7. Let X1, X2,..., Xn be a random sample from f(x; 0) = 0e-O¤I(0,0) (x). Find a 100y or (1 – a)100 percent confidence interval for the mean of the population.
- 3.3.24. Let X1, X2 be two independent random variables having gamma distribu- tions with parameters a₁ = 3, B₁ = 3 and a2 = 5, B2 = 1, respectively. (a) Find the mgf of Y = 2X₁ +6X2. (b) What is the distribution of Y?5. The variance of a random variable X is defined as the expected value of the squared deviation from its mean 4 = EX.ie. Var(X) = E[(X-EX])²]. Show that Var(X) = EX ELX4. Suppose you are required to predict the value of the r.v. X. Assume that you know the distribution of X as well as the mean µ and variance o². Suppose your prediction is a real number 0. The squared error (X - 0)² will be deducted from your paycheck. (a) If your prediction is 0 = 2 and X turns out to be 7, what is error? your squared (b) If your prediction is 0 = 3/4 and X has a Bernoulli distribution with mean 1/3, what is your mean squared error? That is, compute E[(X - 0)²]. (c) If X has a uniform-(0, 1) distribution and your prediction is 0 = 1/3, what is your mean squared error? (d) In general, if you wish to minimize your mean squared error E[(X - 0)²] What should your prediction 0 be? (Hint: There are a variety of ways to solve this, but one way is to start by E[(X - 0)²] = E[((X − µ) + (µ − 0))²1 - and then just continue doing what seems like the obvious next step until you end up with a nice expression for the mean squared error. In this expression it should be easy to see…
- . Let X1, X2, .,X, be a random sample from a normal population with mean u variance o?. Xn and Så are sample mean and variance respectively. According to this information which one of the following is false? a. o2 O b. Vn (Xn-H)~N(0,1) O c. Var(S) = 204 n-1 Od. E(X;) =7 е.8. Similar to Question 6, consider a portfolio with w invested in asset X and 1- w invested in asset Y for w€ (0,1). The volatilities of asset X and Y are 0.2 and 0.3, respectively. Suppose that the correlation coefficient between the two assets is zero. Express the portfolio variance as a function of w and find the value w* that yields the minimum portfolio variance, i.e. o(w*). Select the best answer that corresponds to the minimum portfolio volatility, op(w*): (a) 16.64% (b) 2% (c) 2.77% (d) 14.14% 9. Stock J has a beta of 1, an expected return of 15%. The equity risk premium is 10%, and the risk-free rate is 2.5%. Calculate Jensen's alpha measure for Stock J. (a) -2.5% (b) 0% (c) 2.5% (d) -7.5% 10. Currently, shares of MJ Corp. trade at $100. The probability of the price increasing by $10 in one day is 30% and the probability of the price decreasing by $10 in one day is 70%. Let R₂ denote log-return on the asset over two days, i.e. R₂ = In (a) 12.96% (b) 13.69% (c) 7.69% (d) 20.96%…Q1. Let X and S be the mean and variance of independent random samples of size n; from populations with mean H; and variance of (i = 1, 2), respectively where u, = 20, of = 9, n = 36 and 4z = 18, ož = 16, n2 = 49. Find (using MINITAB or Tables of cdf) a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S{ > s{) = 0.80 e) P(X, - X2 > 0.2336) ) P(S{/S > 0.8368) %3D %3D