ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 25 - 29 of 39

Access detailed explanations (illustrated with images and videos) to 39 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Subscription can be renewed yearly absolutely FREE! View Sample Explanation or View Features.

Rs. 200.00 or

How to register?

Question number: 25

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Edit

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

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

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

Explanation

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

The mean is

… (107 more words) …

Question number: 26

» Statistical Quality Control » Sequential Sampling Plans

Edit

Appeared in Year: 2015

Essay Question▾

Describe in Detail

To test the hypothesis against for the distribution

Develop the sequential probability ratio test.

Explanation

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

Let type I and type II errors are defined as

P (rejecting the lot when θ=θ 0) =α

P (accpeting the lot when θ=θ 1) =β

Under H 0 and H 1 the pmf is

… (140 more words) …

Question number: 27

» Multivariate Analysis » Multivariate Normal Distribution » Partial Correlation Coefficient

Edit

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

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

where these terms are defined by this equation

Given that

… (104 more words) …

Question number: 28

» Multivariate Analysis » Estimation » Covariance Matrix

Edit

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.

from a bivariate normal distribution.

Explanation

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

Assume

So,

… (107 more words) …

Question number: 29

» Estimation » Estimation Methods » Methods of Moments

Edit

Appeared in Year: 2015

Essay Question▾

Describe in Detail

The observations

3.9,2.4,1.8,3.5,2.4,2.7,2.5,2.1,3.0,3.6,3.6,1.8,2.0,4.0,1.5

are a random sample from a rectangular population with pdf

Estimate the parameters by the method of moments.

Explanation

Let X 1, X 2, …, X n be a random sample from a rectangular population. We known that

The estimating equations are

… (104 more words) …