Statistical Inference and Regression Models MCQ part-4

Que.Which of the following theorem states that the distribution of averages of iid variables, properly normalized, becomes that of a standard normal as the sample size increases?
a. Central Limit Theorem
b. Central Mean Theorem
c. Centroid Limit Theorem
d. All of the mentioned
Discussion
Que.The binomial random variables are obtained as the sum of iid Gaussian trials.
a. True
b. False
c. May be True or False
d. Can’t say
Discussion
Que.The _________ of the Chi-squared distribution is twice the degrees of freedom.
a. variance
b. standard deviation
c. mode
d. none of the mentioned
Discussion
Que.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
Discussion
Que.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
Discussion
Que.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
Discussion
Que.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
Discussion
Que.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
Discussion
Que.CLT is mostly useful as an approximation.
a. True
b. False
c. May be True or False
d. Can’t say
Discussion
Que.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
Discussion