Day 9: CFA Level I - Probability Distributions & Sampling Study Plan | 90 Days to CFA Level 1

Today is about probability distributions and sampling—two ideas that show up everywhere in Quant (and later in Fixed Income and Portfolio concepts). 

Disclaimer - This is a study plan and practice guide, not official CFA Institute curriculum material.

Checklist before Studying

• Workspace: one clean page for formulas + one for “common traps.”
• Calculator check: clear TVM registers; confirm STAT functions are working; set decimals to a comfortable default (often 4–6).
• Materials: formula sheet/flashcards, one short notes source, question bank.
• Question bank setup: create a mini-quiz tag set: Normal, Lognormal, t, Chi-square, F, CLT, Sampling distributions.

Daily Ethics reading + prep (15–20 minutes)

• Micro-reading: Professionalism—what it means to act with integrity even when no one is watching.
• Do this: Write a 3–4 line reflection: A friend asks for “inside” exam questions or leaked mocks. How do you respond?
• 5 Ethics warm-up checks:
1. Is it acceptable to use “shared memory dumps” from past candidates?
2. What is the clean alternative when you feel underprepared?
3. What would you do if a study group circulates suspicious material?
4. What is the most professional way to say no?
5. Who could be harmed by unethical shortcuts?

Main study block (75–120 minutes): Distributions & sampling

1) Common distributions (recognition + use cases)

• Normal distribution: symmetry, mean = median = mode, role in z-scores.
• Lognormal distribution: log of variable is normal; why prices/wealth-like variables can be skewed.
• Student’s t-distribution: fatter tails; small samples, unknown variance.
• Chi-square distribution: relates to variance.
• F-distribution: ratio of variances.

2) CLT (Central Limit Theorem) intuition

• The sampling distribution of the sample mean tends toward normal as sample size grows.
• CLT does not make your data normal.
• Why standard errors shrink as sample size rises.

3) Sampling and sampling distributions

• Population vs sample.
• Sampling distribution: distribution of a statistic across many samples.
• Standard error: what it represents and why it matters.
• Pitfalls: SD vs SE; treating one sample as “the truth.”

25-question practice target (20 Quant + 5 Ethics)

Quant (20)

1. Normal distribution & z-scores (6)
2. Lognormal vs normal recognition/interpretation (4)
3. t-, chi-square, F identification/use (4)
4. CLT and sampling distribution concepts (4)
5. Standard error vs standard deviation traps (2)

Ethics (5)

• Professionalism + integrity scenarios (5)

Mistake-log prompt

• Concept gap
• Formula gap
• Calculator error
• Reading error

Five-question review checkpoint

1. In one sentence, what does the CLT tell you about the sample mean?
2. What is the difference between standard deviation and standard error?
3. Give one real-world variable often modelled as lognormal.
4. When might a t-distribution be more appropriate than a normal distribution?
5. What does “sampling distribution of the mean” mean?

• One takeaway + ethics reflection reminder.

Tomorrow preview (Day 10)

Hypothesis testing foundations: null vs alternative, test-statistic intuition, and interpreting results without overthinking the math.