Quiz Details
QZ-20260908-60013
Topics:
Maximum likehood estimators
Calculations
Difficulty:
Level 5 - Very Hard
Questions:
14
Language:
English (English)
Generated:
September 08, 2026 at 11:15 AM
Generated by:
NANZIRI PATIENCE
Instructions: Select an answer for each question and click "Check Answer" to see if you're correct. Then view the explanation to learn more!
1 What is the maximum likelihood estimator (MLE) of the mean of a normal distribution when the variance is known?
Correct Answer:
C
Explanation: The MLE for the mean of a normal distribution with known variance is the sample mean, as it maximizes the likelihood function based on the data.
Explanation: The MLE for the mean of a normal distribution with known variance is the sample mean, as it maximizes the likelihood function based on the data.
2 In a Poisson distribution, what parameter is estimated by the maximum likelihood estimator?
Correct Answer:
D
Explanation: The MLE for a Poisson distribution is the sample mean, which serves as the estimate for the parameter lambda (λ).
Explanation: The MLE for a Poisson distribution is the sample mean, which serves as the estimate for the parameter lambda (λ).
3 If you have a dataset from a Bernoulli distribution, what is the MLE for the probability of success?
Correct Answer:
B
Explanation: The MLE for the probability of success in a Bernoulli distribution is the number of successes divided by the total number of trials.
Explanation: The MLE for the probability of success in a Bernoulli distribution is the number of successes divided by the total number of trials.
4 What is the likelihood function for a normal distribution with unknown mean and known variance?
Correct Answer:
C
Explanation: The likelihood function for a normal distribution with unknown mean is the product of the normal density functions for all observed data points.
Explanation: The likelihood function for a normal distribution with unknown mean is the product of the normal density functions for all observed data points.
5 For a linear regression model, what do the maximum likelihood estimators of the coefficients derive from?
Correct Answer:
A
Explanation: In linear regression, MLE of the coefficients is derived from maximizing the likelihood of the residuals assuming they are normally distributed.
Explanation: In linear regression, MLE of the coefficients is derived from maximizing the likelihood of the residuals assuming they are normally distributed.
6 For a sample of size n from a uniform distribution on [0, θ], the MLE for θ is given by which of the following?
Correct Answer:
C
Explanation: The MLE for θ in a uniform distribution is the maximum observation in the sample, as this is the value that maximizes the likelihood function.
Explanation: The MLE for θ in a uniform distribution is the maximum observation in the sample, as this is the value that maximizes the likelihood function.
7 In the context of MLE, what is the primary purpose of the Fisher Information?
Correct Answer:
D
Explanation: Fisher Information provides the variance of the maximum likelihood estimator, indicating how much information the data carries about the parameter.
Explanation: Fisher Information provides the variance of the maximum likelihood estimator, indicating how much information the data carries about the parameter.
8 What is the MLE for the rate parameter of an exponential distribution given a sample of size n?
Correct Answer:
C
Explanation: The MLE for the rate parameter (λ) of an exponential distribution is given by n divided by the sample mean.
Explanation: The MLE for the rate parameter (λ) of an exponential distribution is given by n divided by the sample mean.
9 Which of the following is a necessary condition for MLE to be consistent?
Correct Answer:
D
Explanation: For MLE to be consistent, the true parameter value must lie in the interior of the parameter space, ensuring that as sample size increases, the estimator converges to the true value.
Explanation: For MLE to be consistent, the true parameter value must lie in the interior of the parameter space, ensuring that as sample size increases, the estimator converges to the true value.
10 When dealing with correlated data, which technique can be used to obtain MLEs?
Correct Answer:
C
Explanation: Generalized least squares accounts for correlation in the data and provides MLEs that are more efficient in such contexts.
Explanation: Generalized least squares accounts for correlation in the data and provides MLEs that are more efficient in such contexts.
11 In logistic regression, which of the following is the primary purpose of the logit link function?
Correct Answer:
B
Explanation: The logit link function transforms probabilities into a linear scale, allowing for the use of linear regression techniques for binary outcomes.
Explanation: The logit link function transforms probabilities into a linear scale, allowing for the use of linear regression techniques for binary outcomes.
12 What is the asymptotic distribution of the MLE under regularity conditions?
Correct Answer:
B
Explanation: Under regularity conditions, the MLE is asymptotically normally distributed, meaning that as sample size increases, the distribution of the MLE approaches a normal distribution.
Explanation: Under regularity conditions, the MLE is asymptotically normally distributed, meaning that as sample size increases, the distribution of the MLE approaches a normal distribution.
13 In the context of MLE, what does the term 'identifiability' refer to?
Correct Answer:
D
Explanation: Identifiability refers to the ability to distinguish between different parameter values based on the data, which is crucial for obtaining valid MLEs.
Explanation: Identifiability refers to the ability to distinguish between different parameter values based on the data, which is crucial for obtaining valid MLEs.
14 When calculating MLE for a binomial distribution, what is typically calculated to find the maximum likelihood estimate?
Correct Answer:
A
Explanation: To find the MLE for a binomial distribution, the log of the likelihood function is typically calculated and maximized with respect to the probability of success.
Explanation: To find the MLE for a binomial distribution, the log of the likelihood function is typically calculated and maximized with respect to the probability of success.