代写ST5222留学生、代做Java/c++，Python程序设计、代写Applied Statistics

日期：2019-10-10 10:08

ST5222: Advanced Topics in Applied Statistics

Midterm 1

Dealine for submission midnight 9th of October, 2019.

1. (10 points)

(a) Suppose (x1, x2, x3) follow a multivariate normal distribution with

mean (µ1, µ2, µ3) and covariance matrix

show that the conditional distribution of (x1, x2) given x3 has

mean vector [µ1 + ρ2(x3 − µ3), µ2]

T and covariance matrix:

(b) If x ∼ Np(µ, Σ) random variables and QΣQT

(q × q) is nonsingular,

then, given Qx = q, show that the conditional distribution

of X is normal with µ + ΣQT(QΣQT)−1(q − Qµ) and covariance

matrix Σ − ΣQT(QΣQT)−1QΣ.

2. (15 points) A naturalist for the Alaska Fish and Game Department

studies grizzly bears with the goal of maintaining a healthy population.

Measurements on n = 61 bears provided the following summary

statistics:

1

Variable Weight Body Neck Girth Head Head

(kg) length (cm) (cm) length width

(cm) (cm) (cm)

Sample

mean x¯ 95.52 164.38 55.69 93.39 17.98 31.13

Covariance matrix:

(a) Perform a principal component analysis using the covariance matrix.

Can the data be effectively summarised in fewer than six

dimensions?

(b) Perform a principal component analysis using the correlation matrix.

(c) Comment on the similarities and differences between the two analyses.

3. (15 points) Consider the data in file data3.txt. Cluster the data using

K-means method. Comment on your findings.

2