DTSA 5001 - Probability Theory: Foundation For Data Science Exam Questions And ANSWERs |Graded A+

1. The set of all possible outcomes of a random experiment is called the: a) Event b) Sample Space c) Probability Set d) Outcome Collection ANSWER: b) Sample Space 2. Two events A and B are mutually exclusive. What is P(A ∩ B)? a) P(A)P(B) b) P(A) + P(B) c) 0 d) 1 ANSWER: c) 0 3. A probability distribution where each outcome is equally likely is called: a) Conditional b) Uniform c) Normal d) Binomial ANSWER: b) Uniform 4. If the probability of event A is 0.3, what is P(A^c), the probability of the complement? a) 0.3 b) 0.7 c) 0.0 d) 0.5 ANSWER: b) 0.7 5. The function that describes the probability of a discrete random variable taking on a specific value is called the: a) Cumulative Distribution Function (CDF) b) Probability Density Function (PDF) c) Probability Mass Function (PMF) d) Likelihood Function ANSWER: c) Probability Mass Function (PMF) 6. For two independent events A and B, which rule applies? a) P(A ∩ B) = P(A) + P(B) b) P(A ∩ B) = P(A | B)P(B) c) P(A ∩ B) = P(A)P(B) d) P(A ∪ B) = P(A)P(B) ANSWER: c) P(A ∩ B) = P(A)P(B) 7. The probability of event A given that event B has occurred is written as: a) P(A ∩ B) b) P(A | B) c) P(B | A) d) P(A ∪ B) ANSWER: b) P(A | B) 8. According to Bayes' Theorem, P(A|B) is equal to: a) [P(B|A)P(A)] / P(B) b) P(B|A)P(A) c) P(A ∩ B) / P(A) d) P(B) / P(A) ANSWER: a) [P(B|A)P(A)] / P(B) 9. A random variable that can take on any value in an interval is called: a) Discrete b) Continuous c) Categorical d) Ordinal ANSWER: b) Continuous 10. The expected value of a random variable is its: a) Most likely value b) Long-run average value c) Median value d) Standard deviation ANSWER: b) Long-run average value 11. The variance of a random variable measures its: a) Average value b) Spread or dispersion c) Skewness d) Central tendency ANSWER: b) Spread or dispersion 12. The square root of the variance is the: a) Mean b) Standard Deviation c) Covariance d) Expectation ANSWER: b) Standard Deviation 13. A Bernoulli random variable has how many possible outcomes? a) 0 b) 1 c) 2 d) n ANSWER: c) 2 14. The distribution that models the number of successes in n independent Bernoulli trials is the: a) Poisson Distribution b) Geometric Distribution c) Binomial Distribution d) Normal Distribution ANSWER: c) Binomial Distribution 15. The probability distribution of the number of trials needed to get the first success in a sequence of independent Bernoulli trials is the: a) Binomial Distribution b) Geometric Distribution c) Negative Binomial Distribution d) Hypergeometric Distribution ANSWER: b) Geometric Distribution 16. The distribution often used to model the number of events occurring in a fixed interval of time or space is the: a) Binomial Distribution b) Poisson Distribution c) Exponential Distribution d) Uniform Distribution ANSWER: b) Poisson Distribution 17. The continuous distribution characterized by a bell-shaped curve is the: a) Uniform Distribution b) Exponential Distribution c) Normal Distribution d) Gamma Distribution ANSWER: c) Normal Distribution 18. For a standard normal distribution (Z), the mean and variance are: a) μ=0, σ²=0 b) μ=0, σ²=1 c) μ=1, σ²=0 d) μ=1, σ²=1 ANSWER: b) μ=0, σ²=1 19. The rule that states for a large sample, the distribution of the sample mean is approximately normal is the: a) Law of Large Numbers b) Bayes' Rule c) Central Limit Theorem d) Empirical Rule ANSWER: c) Central Limit Theorem 20. Covariance measures: a) The variance of a single variable. b) The direction of the linear relationship between two variables. c) The strength of a non-linear relationship. d) The mean of a product of two variables. ANSWER: b) The direction of the linear relationship between two variables. 21. Correlation is a standardized version of: a) Variance b) Expectation c) Covariance d) Standard Deviation ANSWER: c) Covariance 22. The correlation coefficient always lies between: a) -1 and 0 b) 0 and 1 c) -∞ and ∞ d) -1 and 1 ANSWER: d) -1 and 1 23. If two random variables are independent, their covariance is: a) 0 b) 1 c) -1 d) The product of their variances ANSWER: a) 0 24. The probability of the union of two events, P(A ∪ B), is given by: a) P(A) + P(B) b) P(A) + P(B) - P(A ∩ B) c) P(A)P(B) d) P(A | B)P(B) ANSWER: b) P(A) + P(B) - P(A ∩ B)