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# MCQs on Likelihood

The _________ of the Chi-squared distribution is twice the degrees of freedom.

a) variance

b) standard deviation

c) mode

d) none of the mentioned

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Answer: a

Explanation: The mean of the Chi-squared is its degrees of freedom.

Point out the correct statement.

a) Asymptotics are incredibly useful for simple statistical inference and approximations

b) Asymptotics often lead to nice understanding of procedures

c) An estimator is consistent if it converges to what you want to estimate

d) All of the mentioned

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Answer: d

Explanation: Consistency is neither necessary nor sufficient for one estimator to be better than another.

Gosset’s distribution is invented by which of the following scientist?

a) William Gosset

b) William Gosling

c) Gosling Gosset

d) All of the mentioned

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Answer: a

Explanation: Gosset’s distribution is indexed by a degrees of freedom.

The _________ of a collection of data is the joint density evaluated as a function of the parameters with the data fixed.

a) probability

b) likelihood

c) poisson distribution

d) all of the mentioned

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Answer: b

Explanation: Likelihood analysis of data uses the likelihood to perform inference regarding the unknown parameter.

Point out the wrong statement.

a) Asymptotics generally give assurances about finite sample performance

b) The sample variance and the sample standard deviation are consistent as well

c) The sample mean and the sample variance are unbiased as well

d) None of the mentioned

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Explanation: The kinds of asymptotics that do are orders of magnitude more difficult to work with.

Which of the following is a property of likelihood?

a) Ratios of likelihood values measure the relative evidence of one value of the unknown parameter to another

b) Given a statistical model and observed data, all of the relevant information contained in the data regarding the unknown parameter is contained in the likelihood

c) The Resultant likelihood is multiplication of individual likelihood

d) All of the mentioned

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Answer: d

Explanation: Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome.

CLT is mostly useful as an approximation.

a) True

b) False

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Answer: a

Explanation: The CLT applies in an endless variety of settings.

The beta distribution is the default prior for parameters between ____________

a) 0 and 10

b) 1 and 2

c) 0 and 1

d) None of the mentioned

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Answer: c

Explanation: Bayesian statistics posits a prior on the parameter of interest.

Which of the following mean is a mixture of the MLE and the prior mean?

a) interior

b) exterior

c) posterior

d) all of the mentioned

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Answer: c

Explanation: MLE stands for maximum likelihood.

Usually replacing the standard error by its estimated value does change the CLT.

a) True

b) False

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Answer: b

Explanation: Usually replacing the standard error by its estimated value doesn’t change the CLT.