# 代写Stat 445程序、代做MATLAB程序

 Stat 445, spring 2020, Homework assignment 1 04/02/2020 Question 1 (problem 4.3 of text) Let X et N3(μ, Σ) with μ = ?? 314 ?? and Σ = ?? 1 2 0 2 5 0 0 0 2 ?? Which of the following random variables are independent? Explain? a. X1 and X2. b. X2 and X3 c.(X1, X2) and X3 c. X1+X2 2 and X3 d. X2 and X2 52X1 X3 Question 2 (problem 4.16 from the text) 代写Stat 445作业、代做MATLAB程序语言作业、MATLAB,python设计作业代写Let X1, X2, X3 and X4 be independent Np(μ, Σ) random vectors. a. Find the marginal distributions for each of the random vectors V1 = X1/4 X2/4 + X3/4 X4/4 V2 = X1/4 + X2/4 X3/4 X4/4 b. Find the joint density of the random vectors V1 and V2 defined in part (a). Question 3 (problem 4.21 from the text) Let X1, . . . , X60 be a random sample of size 60 from a four-variate normal distribution with mean μ and covariance Σ. Specify each of the following completely. a. The distribution of Xˉ b. The distribution of (X1 μ)T Σ 1(X1 μ) c. The distribution of n(Xˉ μ)T Σ 1(Xˉ μ) d. The distribution of n(Xˉ μ)T S 1(Xˉ μ) Question 4 (problem 4.22 from the text) Let X1, . . . , X75 be a random sample from a population distribution with mean μ and covariance Σ. What is the approximate distribution of each of the following? a. Xˉ b. n(Xˉ μ)T S 1(Xˉ μ) 1 Question 5 (problem 5.1 from the text) a. Evaluate T2 for testing H0 : μ =  7 11  using the data X = ???? 2 12 8 9 6 9 8 10 ???? b. Specify the distribution of T2 for the situation in (a). c. Using (a) and (b), test H0 at the α = 0.05 level. What conclusion do you reach? Question 6 (problem 5.2 from the text) The data in Example 5.1 are as follows. ?? 6 9 10 6 8 3 ?? . Verify that T2 remains unchanged if each observation xj , j = 1, 2, 3 is replaced by Cxj and μ0 is replaced by Cμ0, where C =  1 1 1 1  . Note that the transformed data matrix is ?? (6 9) (6 + 9) (10 6) (10 + 6) (8 3) (8 + 3) 如有需要，请加QQ：99515681 或邮箱：99515681@qq.com 微信：codehelp
免责声明：珠穆朗玛网对于有关本网站的任何内容、信息或广告，不声明或保证其正确性或可靠性，用户自行承担使用网站信息发布内容的真假风险。