Learning Targets - APMA Probability F25

Basics of Probability (Chapters 1-2)

1. I can find basic probabilities of events from an equally likely sample space, including compound events (1.1-1.3)
2. I can calculate conditional and total probabilities for sequential experiments, using tree diagrams, the Law of Total Probability, and Bayes’ Theorem. (1.4-1.6, 2.1)
3. I can use counting techniques to find the size of a set and use it to compute probabilities for an equally likely sample space. (e.g. orderings, permutations, combinations, sampling with and without replacement) (2.2)
4. I can determine the reliability of systems with components in parallel and/or series (2.3,2.4)

Discrete and Continuous RVs (Chapters 3-4)

5. I can model a discrete random variable with a PMF and CDF and use it to compute probabilities, expected values, variances, and standard deviations. (3.1-3.2, 3.4-3.5)
6. I can identify and compute probabilities for Bernoulli, Binomial, Geometric, and Pascal random variables (3.3)
7. I can model a continuous random variable with a PDF and a CDF and use it to compute probabilities, expected values, variances, and standard deviations. (4.1-4.4)
8. I can model a Poisson process using poisson and exponential random variables and use them to analyze the process. (3.3, 4.5)
9. I can find and work with probabilities for a normal random variable. (4.6)
10. I can find the PDF, CDF, and expected value of a function of one random variable. (3.6-3.8, 6.2)

Joint Distributions and Conditioned RVs (Chapters 5-7)

11. I can model a pair of discrete random variables with a joint PMF and use it to compute probabilities, marginal PMFs, expected values, and the covariance. (5.1-5.3, 5.6, 5.8)
12. I can model a pair of continuous random variables with a joint PDF and use it to compute probabilities, marginal PDFs, expected values, and the covariance. (5.4, 5.5, 5.6, 5.8)
13. I can find the $PMF/PDF$ and expected value of a function of two random variables. (5.7, 6.1, 6.4, 6.5)
14. I can find probabilities and the expected value of a random variable conditioned on an event or on another random variable. (7.1, 7.2, 7.4, 7.5)

Estimation, Bounds, and Hypothesis Testing

15. I can demonstrate understanding of the Central Limit Theorem and knowledge of when and how it is appropriate to use it in applications. (9.1, 9.5, 10.1)
16. I can use Markov’s and Chebyshev’s Inequalities and the Law of Large Numbers to estimate or bound probabilities for random variables (10.2, 10.3)
17. I can design a significance test for a claimed probability model (11.1)
18. I can design a binary hypothesis test to decide between two probability models. (11.2)
19. I can find both minimum MSE and linear estimates for a random variable given the value of another random variable. (12.1, 12.2)