Review & Cheat Sheet
[!IMPORTANT] Key Goal: Ensure you can distinguish between Discrete and Continuous distributions and know when to apply Gaussian, Beta, or Gamma.
1. Key Takeaways
- Discrete vs Continuous:
- Discrete (PMF): Sums to 1. Used for countable outcomes (Coin flips, Emails).
- Continuous (PDF): Integrates to 1. Area under curve = Probability. Used for measurable outcomes (Height, Time).
- The Gaussian King:
- Symmetric, Bell-shaped. Defined by Mean (μ) and Std Dev (σ).
- 68-95-99.7 Rule describes the spread.
- Z-score: Standardizes any normal distribution to N(0, 1).
- The Flexible Friends:
- Beta: Bounded [0, 1]. Models probabilities/proportions. “Conjugate Prior” for Binomial.
- Gamma: Bounded [0, ∞). Models waiting times for k events.
2. Interactive Flashcards
Test your knowledge! Click a card to flip it.
PMF vs PDF
Click to flip
PMF is for Discrete (P(X=x)). PDF is for Continuous (Area under curve).
What is a Z-Score?
Click to flip
It measures how many standard deviations a data point is from the mean. Z = (x - μ) / σ
Beta Distribution Use Case?
Click to flip
Modeling probabilities or proportions (bounded [0, 1]). E.g., CTR, Conversion Rate, Bayesian Priors.
Gamma vs Exponential?
Click to flip
Exponential is waiting time for 1 event. Gamma is waiting time for k events.
Why use Log-Probabilities?
Click to flip
To avoid underflow (tiny numbers becoming 0) and overflow (factorials) when calculating with many probabilities.
3. Cheat Sheet
| Distribution | Type | Range | Parameters | Interpretation |
|---|---|---|---|---|
| Bernoulli | Discrete | {0, 1} | p | Single trial (Success/Fail) |
| Binomial | Discrete | {0..n} | n, p | Count successes in n trials |
| Poisson | Discrete | {0..∞} | λ | Count events in fixed interval |
| Gaussian | Continuous | (-∞, ∞) | μ, σ | Natural variation, Sum of errors (CLT) |
| Beta | Continuous | [0, 1] | α, β | Probability of a probability |
| Gamma | Continuous | [0, ∞) | k, θ | Waiting time for k events |
4. Next Steps
Now that you understand the fundamental distributions, you’re ready to explore how they interact in higher dimensions.