ISS Statistics Paper II (Old Subjective Pattern): Questions 1 - 8 of 39

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Question number: 1

» Statistical Quality Control » Sequential Sampling Plans

Appeared in Year: 2015

Essay Question▾

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Distinguish between the single sampling plan and double sampling plan. Discuss how the O. C curves can be used for comparing two sampling plans.

Explanation

A single sampling plan in which a decision about the acceptance or rejection of a lot is based on one sample that has been inspected where double sampling plan when a decision about the acceptance or rejection of a lot has not been reached after single sample inspection from a… (282 more words) …

Question number: 2

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2015

Essay Question▾

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Derive the likelihood ratio test for comparing the means of k independent homoscedastic normal populations.

Explanation

Given that there are k independent homoscedastic normal populations that is the variance is same i. e. Xi~N(μi,σ2); i = 1, 2, …, k. We have to test

H0:μ1=μ2==… (806 more words) …

Question number: 3

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2014

Essay Question▾

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Define completeness. Verify whether Bin (1, p) is complete.

Explanation

Completeness: It is a property of a statistic in relation to a model for a set of observed data. In essence, it is a condition which ensures that the parameters of the probability distribution representing the model can all be estimated on the basis of the statistic: it ensures… (541 more words) …

Question number: 4

» Estimation » Estimation Methods » Methods of Moments

Appeared in Year: 2014

Essay Question▾

Describe in Detail

For the Pareto distribution with pdf

f(x;λ)=λxλ+1x1,λ>0

Show that method of moments fails if 0 < λ < 1. State the method of moments estimator when λ > 1. Is it consistent? Justify your answer.

Explanation

Let X 1 , X 2 , …, X n be a simple random sample of Pareto random variables with density

f(x;λ)=λxλ+1x1,λ>0

The mean and variance are respectively

μ=λλ… (197 more words) …

Question number: 5

» Estimation » Estimation Methods » Methods of Moments

Appeared in Year: 2014

Essay Question▾

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X 1, X 2, …, X n be a random sample from U (0, θ). Obtain the moment estimator of θ. Also find its variance.

Explanation

Let X 1, X 2, …, X n be a random sample from U (0, θ). We known that

μ1=θ2=m1

The estimating equation is

m1=1ni=1nXi=θ… (137 more words) …

Question number: 6

» Linear Models » Theory of Linear Estimation » Gauss-Markoff Setup

Appeared in Year: 2014

Essay Question▾

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Define estimability of a linear parametric function in a Gauss Markov model. State and prove a necessary and sufficient condition for estimability.

Explanation

Estimability : The linear parametric function c’β is an estimable function if there exists a vector

a R n such that

E(ay)=cβforanyβ

If X is of full column rank then all linear combinations of… (226 more words) …

Question number: 7

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

Essay Question▾

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X 1 , X 2 , …, X n are i. i. d. random variables from N (θ, 1) where θ is an integer. Obtain MLE of θ.

Explanation

X 1 , X 2 , …, X n are i. i. d. random variables from N (θ, 1). The density function of X is

fX(x)=12πexp(12(xθ)2)

The likelihood… (183 more words) …

Question number: 8

» Hypotheses Testing » Hypothesis » Composite

Appeared in Year: 2014

Essay Question▾

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A sample of size n from normal distribution N (θ, σ 2 ) with σ 2 =4 was observed. 95 % confidence interval for θ was computed from the above sample. Find the value of n if the confidence interval is (9.02, 10.98).

Explanation

The Margin of error is defined as

E=zα/2σn

Where z α/2 is the critical value = 1.96

σ is the standard deviation = 2

E is the margin of error= Differencebet… (51 more words) …

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