Assume the full model is Yij = µ + αi + €ij , i = 1, 2, 3. Check to see if the following parameters are estimable or not (YES/No)?
1. (µ + α1) −[(µ+α2)+(µ+α3)]/2 or α1 −(α2+α3)/2
2. (µ + α1) − (µ + α2) , (or α1 − α2);
3. α1 + α2.
Exercice 1: Consider a random variable X with the following probabilities distribution: 2 where α1 and α2 are parameters such that 0 < αι < 1,0 < α2 < 1 and αί+a2 1. 1) Compute E[X] and E[X21. 2) Find aǐ and , two estimators of α1 and α2, using the Method of Moments. 3) We assume that: 7t 7 1 1-1 i=1 is as unbiased?
Exercise 1: Probability Distribution
Please give detailed steps for questions 2 & 3, I have seen
the explanation before but it remains unclear.
Exercice 1 Consider a random variable X with the following probabilities distribution: where α1 and α2 are parameters such that 0 < αι < 1,0 < α2 1 and α1taz 1. 1) Compute E[X] and E[X2]. 2) Find a. and az, two estimators of«, and α2, using the Method of Moments. 3)we assume that 22-1-12,xf 7t 6,...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0
Consider the manipulator with DH parameters below i ai di αi 1 a1 d1 0 2 0 0 π/2 3 a3 0 −π/2 Draw the mechanism in its zero-angle position. Label all zi and xi axes, and non-zero length parameters. Given the position 0d03 of the last frame with respect to the base frame, find the joint angles. Make sure to identify multiple solutions.
please don't copy. thx
Question 1. Consider the model Yij = Mi + Rij, Rij~N(0,02), i = 1,2;j = 1,2, ..., Ni. 222(Y1j-81+)? Part A. Show that Sị is an unbiased estimator of o2. Part B. Show that the pooled estimate of o2 is unbiased. n1-1
7. Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.9 8% 17% B 1.3 12 8 C 1.7 16 11 a. If σM = 12%, calculate the...
10. Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.8 10% 25% B 1.0 12 10 C 1.2 14 20 a. If σM = 20%,...
3. In the CRD model Xy-μ+1+ 4,i-1, independently. Then showing all steps. find ri, we assume that etj ~ Normal(0,02) ,v,, -1, (a) the distribution of Yij (b) the distribution of Y. (e) the distribution of Y (d) cov(Y.,Y,) (e) cov( (f) cov(A, A)
2. (a) Let us consider a full model of a balanced (all t treatments have equal number of observations r) CRD design with t treatments and r replications of each treatment, hence having n-rt observations i. Minimizing sum of square error Δfull(μ, Tỉ)-Σι-12jai (Vij-l-ri)2 with respect to μ and Ti find the least square estimators of μ and Te as μ and Ti Hint: Take derivative of the objective function with respect to u and Ti and equate then to...