Study Guide for Exam 2

Auburn University Department of Mathematics and Statistics

Stat 2510 Study Guide for Unit 2 Exam and RStudio Quiz

Exam Recommendation

• Study course material including lecture notes and homework assignments before attempting the practice exam.

• Pay special attention to the listed tasks to prepare.

• Use the practice test to identify areas of strength and weakness.

Exam Format

• Traditional multiple-choice, pen(cil)-and-paper exam.

• Indicate your letter answer on the blank on the cover page.

• No Scantron forms or personal paper allowed; scratch paper will be provided.

Date and Location

• Date: Wednesday, March 5

• Time: 2:00 PM to 2:50 PM

• Time limit: 50 minutes

End of Unit 2 RStudio Quiz

• Conducted online via MyLab Statistics, using RStudio.

• Open Book: You can refer to notes.

• Time Limit: 60 minutes, single attempt only.

• Available from Wednesday, March 5 at 3 PM to Thursday, March 6 at 11 PM.

Unit 2 Exam Policies

• Required to carry and show Student ID card upon request.

• No books, notes, or electronic devices allowed during the exam.

• A scientific calculator is required; cellphone calculators are not permitted.

Unit 2 Exam Topics

1. Relative frequency interpretation of probability.

2. Calculate probabilities for equally likely outcomes.

3. Calculate conditional probability P(A|B) with sufficient information about A and B.

4. Use the multiplication rule to find P(A and B) when P(A|B) and P(B) are given.

5. Calculate event probability using Bayes' Rule.

6. Probability of a sequence of independent events.

7. Express events using random variables and vice versa.

8. Calculate and interpret mean, variance, and standard deviation of discrete random variables.

Additional Exam Topics

9. Determine if a random variable's distribution is binomial.

10. Find expected value and variance of linear combinations of random variables.

11. Calculate standard deviation from variance.

12. Event probabilities with discrete random variable distributions from tables.

13. Event probabilities for continuous random variable distributions with linear density functions.

14. Characteristics of a known Normal Distribution.

15. Use empirical rule (68-95-99.7 rule) to find proportions relative to mean.

16. Find and interpret z-scores as measures of relative standing.

RStudio Quiz Preparation

1. Import data from a file or via code chunks.

2. Create contingency tables to calculate probabilities.

3. Calculate binomial probabilities using pbinom() and dbinom() functions.

4. Verify approximate Normal Distributions with hist() and qqnorm().

5. Calculate Normal Distribution probabilities with pnorm().

6. Find percentiles and z-values using qnorm().

Important Formulas

• For discrete random variable X:

  • Mean: µ = E(X) = Σ [x * p(x)]

  • Variance: σ² = Var(X) = Σ [(x - µ)² * p(x)]

• If X ∼ Bin(n, p):

  • Mean: µ = E(X) = np

  • Variance: σ² = np(1 - p)

  • Standard deviation: σ = √(np(1 - p))

Probability Rules

• For any two events A and B:

  • Union: P(A or B) = P(A) + P(B) - P(A and B)

  • Complement: P(A) = 1 - P(Aᶜ)

  • Conditional Probability: P(A|B) = P(A and B) / P(B)

  • General Multiplication Rule: P(A and B) = P(A|B)P(B) = P(B|A)P(A)

Definitions

• Independent Events: Events A and B are independent if P(A and B) = P(A)P(B).

• Expected Value of Linear Combinations:

  • E(aX + b) = aE(X) + b

  • E(aX + bY) = aE(X) + bE(Y)

Variance of Linear Combinations

• V(aX + b) = a²Var(X)

• V(aX + bY) = a²Var(X) + b²Var(Y)

Empirical Rule

• 68% of data within 1 standard deviation of the mean.

• 95% within 2 standard deviations.

• 99.7% within 3 standard deviations.

Bayes' Rule Problem Solving Steps

1. Draw tree diagram with given probabilities.

2. Fill in missing probabilities using complementary event rules.

3. Write conditional probability needed and evaluate using the tree diagram.