ISS Statistics Paper II (Old Subjective Pattern): Questions 33 - 37 of 39

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 39 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 200.00 or

Question number: 33

» Hypotheses Testing » Unbiased Test

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Explain the notion of unbiasedness with regards to a test of a hypothesis. Examine the validity of the statement. A most powerful test is invariably unbiased.

Explanation

A test T of the null hypothesis H0:θϵΘ0vsH1:θϵΘ1 is said to be an unbiased test if the probability of rejection H 0 when it is false is at least as much as the probability of… (173 more words) …

Question number: 34

» Estimation » Optimal Properties » Minimum Variance Bound Estimators

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X 1, X 2, …, X n be a random sample from the probability distribution with density

fX(x,θ)=1θexθ;0<x<

= 0; otherwise

where 0 < θ < ∞. Show that X=1ni=1nXi is a minimum variance bound estimator and has variance θ2n .

Explanation

By using Cramer-Rao lower bound we find the minimum variance

fX(x,θ)=1θexθ

logfX(x,θ)=logθxθ

θlogfX(x,θ)… (191 more words) …

Question number: 35

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X 1, X 2, … X n be a random sample from the binomial distribution with probability mass function

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

Examine whether the statistic T=i=1nXi is complete for this distribution.

Explanation

We know that T=i=1nXi is sufficient statistic for this distribution. Then,

f(x_,θ)=θi=1nxi(1θ)ni=1nxi

p… (226 more words) …

Question number: 36

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Appeared in Year: 2015

Essay Question▾

Describe in Detail

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) …

Question number: 37

» Multivariate Analysis » Principal Components » Correlations

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let

Σ=(311131115)

Determine

(i) The principal components y 1, y 2 and y 3.

(ii) The proportion of variance explained each one of them.

(iii) Correlation between the first principal components y 1 and the third original random variable.

Explanation

First find the eigen value and eigen vector pairs

ΣIλ=0

3λ1113λ1115λ=0

(3λ)[(3λ)(5λ)1… (525 more words) …

f Page
Sign In