MSC QUIZ 4

1) What is the sample space of an experiment?

• • A) The set of all possible outcomes of the experiment

• • B) The probability of an event occurring

• • C) The subset of favorable outcomes

• • D) The likelihood of mutually exclusive events

2) What is the birthday paradox concerned with?

• • A) The probability of birthdays on public holidays

• • B) Probability that everyone in a group has a unique birthday

• • C) The likelihood of any individual’s birthday falling in January

• • D) Probability that two people in a group share the same birthday

3) Which of the following is an application of Bayes’ Theorem?

• • A) Counting the outcomes in a sample space

• • B) Calculating conditional probabilities

• • C) Determining the independence of two events

• • D) Evaluating combinatorial outcomes

4) The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as:

• • A) The sample size decreases

• • B) The population mean decreases

• • C) The number of samples increases

• • D) The population standard deviation increase

5) Which of the following distributions is often used in hypothesis testing for sample variances?

• • A) t-distribution

• • B) F-distribution

• • C) Binomial distribution

• • D) Geometric distribution

6) Which of the following tests is non-parametric?

• • A) t-test

• • B) Chi-square test

• • C) Z-test

• • D) Mann-Whitney U test

7) A Markov chain is characterized by which of the following properties?

• • A) Independence of each event

• • B) Dependence on the current state only

• • C) Dependence on all past states

• • D) Randomness of outcomes only

8) A stationary distribution of a Markov chain is a probability distribution that:

• • A) Changes over time

• • C) Depends only on the initial state

• • C) Remains constant over time

• • D) Cannot be calculated for finite chains

9) Which of the following best describes the “states” in a Markov chain?

• • A) Possible positions or conditions in which the process can be

• • B) Outcomes that cannot be visited again

• • C) Sets of independent events

• • D) Independent realizations of random variables

10) If the p-value is 0.03 and the significance level (α) is 0.05, what decision should be made?

• • A) Fail to reject the null hypothesis

• • B) Reject the null hypothesis

• • C) Accept the null hypothesis

• • D) Decrease the sample size