ISS Statistics Paper II (Old Subjective Pattern): Questions 24 - 28 of 39

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Question number: 24

» Statistical Quality Control » Concepts of ATI

Appeared in Year: 2015

Essay Question▾

Describe in Detail

For a sequential probability ratio test of strength (α, β) and stopping bounds are A and B (B < A), show that A ≤ 1-β/α and B ≥ β/1-α

Explanation

Let X= (X 1, …, X k) and also let E k be the set of all points in k dimensional Euclidean space R k, for which we reject H 0 using the sequential probability ratio test. Also, let F k be the set of all points… (315 more words) …

Question number: 25

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Appeared in Year: 2015

Essay Question▾

Describe in Detail

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: 26

» Statistical Quality Control » Sequential Sampling Plans

Appeared in Year: 2015

Essay Question▾

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To test the hypothesis H0:θ=θ0 against H1:θ=θ1 for the distribution

f(x,θ)={θx(1θ)1x;x=0, 1;0<θ<10;otherwise

Develop the sequential probability ratio test.

Explanation

Let x 1, x 2, …, x n are independently and identically distributed with distribution is

f(xi,θ)=i=1nθxi(1θ)1xi

Let type I and type II errors… (502 more words) …

Question number: 27

» Multivariate Analysis » Multivariate Normal Distribution » Partial Correlation Coefficient

Appeared in Year: 2015

Essay Question▾

Describe in Detail

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: 28

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Find the maximum likelihood estimator of the 2×1 mean vector µ and the 2×2 covariance matrix ∑ based on the random sample.

X=[34546477]

from a bivariate normal distribution.

Explanation

We known that the maximum likelihood estimator of multivariate normal distribution is

μ=X_andΣ=i=1n(X_iX_)(X_iX_)n

Assume

X_… (206 more words) …

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