اسم MCQs - قواعدِ اردو

1

Which condition for central limit theorems is stronger (i.e., implies) the Lindeberg condition for triangular arrays of independent variables?

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Kolmogorov condition B Cramér condition C Lyapunov condition D Markov condition

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2

In a chi-square goodness-of-fit test for k categories where m parameters are estimated from the data, the appropriate degrees of freedom is:

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A k B k − 1 − m C k − m D k + m − 1

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3

A weakly stationary (covariance-stationary) time series requires which of the following properties?

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Autocovariance depends on time t and lag k separately B Mean can be a deterministic trend but variance must be infinite C Only that the series be ergodic D Constant mean and autocovariance that depends only on the lag (not on time)

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4

With a Binomial(n,p) likelihood and a Beta(α,β) conjugate prior for p, the posterior distribution for p is:

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Normal with mean α/(α+β) B Gamma with parameters α+n and β C Beta(α+number of successes, β+number of failures) D Binomial with updated sample size n+α+β

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5

Under the Gauss–Markov theorem, the ordinary least squares (OLS) estimator is BLUE (best linear unbiased estimator) provided which set of conditions holds?

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Errors are normally distributed and predictors are independent B Errors have zero mean, are homoscedastic and uncorrelated, and regressors have full rank C Errors are heteroscedastic but mean zero D Predictors are fixed at observed values and errors have any finite variance

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6

Which of the following is NOT an assumption required for one-way ANOVA?

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Equal sample sizes across the groups B Independence of observations C Normality of errors within groups D Homogeneity of variances across groups

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7

Which of the following is the correct interpretation of a p-value in hypothesis testing?

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A The probability that the null hypothesis is true given the data B The probability that the alternative hypothesis is true C The probability of committing a Type II error D The probability of obtaining data as extreme as observed or more so, assuming the null hypothesis is true

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8

Which estimator attains the Cramér–Rao lower bound (is efficient) for estimating the mean μ of N(μ,σ^2) when σ^2 is known?

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Sample median B Sample variance C Sample mean X̄ D Any unbiased linear combination of observations

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9

For a random sample X1,...,Xn drawn from a Poisson(λ) distribution, the maximum likelihood estimator (MLE) of λ is:

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A The sample median B The sample mean (ΣXi/n) C The sample variance (Σ(Xi−X̄)²/(n−1)) D Zero if any Xi=0

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10

According to the Central Limit Theorem, the sampling distribution of the sample mean X̄ for a large sample size n from any population with finite mean μ and variance σ^2 tends to:

Concept: #اسم #قواعدِاردو #اردو(GeneralUrdu)

A Approximately normal with mean μ and variance σ^2/n B A t-distribution with n−1 degrees of freedom C A Poisson distribution with parameter μ D A uniform distribution on [0,1]

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