Multivariate Analysis-Multivariate Normal Distribution (ISS Statistics Paper II (Old Subjective Pattern)): Questions 1 - 3 of 3

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Question number: 1

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Appeared in Year: 2015

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Let X= (X 1, X 2, X 3) ’ be distributed as N 3 (µ, ∑) where µ’= (2, -3, 1) and

Σ=(111132122)

(i) Find the distribution of 3X 1 -2X 2 +X 3.

(ii) Find a 2 × 1 vector a such that X 2 and X2a(X1X2) are independent.

Explanation

(i) the distribution of 3X 1 -2X 2 +X 3 is

Y=3X12X2+X3=(321)(X1X2X3)=AX_

The mean is

E(Y)=… (302 more words) …

Question number: 2

» Multivariate Analysis » Multivariate Normal Distribution » Partial Correlation Coefficient

Appeared in Year: 2015

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Let X = (X 1, X 2, X 3) ’ be distributed as N 3 (µ, ∑) where µ = (10, -7, 2) ’ and

Σ=(213153335)

Find the partial correlation between X 1 and X 2 given X 3.

Explanation

The partial correlation between X 1 and X 2 given X 3 is defined as

rX1X2.X3=sX1X2.X3sX1X1.X3sX2X2.X3

where these… (175 more words) …

Question number: 3

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Appeared in Year: 2015

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Let X 1, X 2, …, X n be a random sample from an NP(μ_,Σ) population with Σ , a positive definite matrix. Derive 100 (1-α) % simultaneous confidence interval for l_μ_ for all l_ϵIRP{0_} .

Explanation

Let X 1, X 2, …, X n be a random sample from an NP(μ_,Σ) and assume the linear combination of the random sample is

Y_=l1X_1+l2X_2+… (264 more words) …

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