Statistics Exam Review

Correlation Coefficient: Understand the calculation using the formula:
r = \frac{\sum (xi - \bar{x})(yi - \bar{y})}{\sqrt{\sum (xi - \bar{x})^2 \sum (yi - \bar{y})^2}}
- Summation of products and squares is essential.
R-Hat Equation: The line of best fit model described by:
\hat{y} = b1x + b0
- Here,
  - b_1 is the slope:
  - b0 is the y-intercept calculated as: b0 = \bar{y} - b_1 \bar{x} .
Standard Deviation: Measure of data variability, calculated as:
s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}

Permutations vs Combinations:
- Use permutations when order matters:
  P(n, r) = \frac{n!}{(n-r)!} - e.g., arranging 15 items taken 3 at a time.
- Use combinations when order does not matter:
  C(n, r) = \frac{n!}{r!(n-r)!}
- e.g., selecting 10 from 5.

The sum of probabilities should equal one; investigate anomalies if the sum exceeds or falls short of this threshold.
To calculate combined probabilities:
- For "AND" scenarios, multiply individual probabilities.
- For "OR" scenarios, add individual probabilities and subtract overlaps if necessary:
- P(A \cup B) = P(A) + P(B) - P(A \cap B)

Expected Value:
E(X) = \sum (xi \cdot p(xi))
where xi is outcome, and p(xi) is corresponding probability.
Variance Calculation:
\sigma^2 = \sum (xi - \mu)^2 \cdot p(xi)
- Variance must consider differences from mean.
Binomial Distribution:
To find P(x = k) in a binomial:
P(X = k) = C(n, k) p^k(1-p)^{n-k}
where C(n, k) represents combinations, and p denotes success probability.

Usage of Calculator: Familiarize with needed functions (binomial calculations).
Exam Format: Expect multiple-choice questions, focus on showing workings where applicable.
- Practice by solving previous problems and example distributions.
Time Management: Allocate time for each question, avoid spending too long on challenging queries.

Create study groups to discuss concepts.
Utilize office hours for clarification on topics.
Ensure comfort with statistical tables and calculator functions before the exam.