CFA Level I - Quantitative Methods Glossary flashcards

Question 1

Combination (nCr)

Accepted Answer

n!/(r!(n−r)!). The number of ways to choose r objects from n when order does not matter.

Question 2

Chi-Square Distribution

Accepted Answer

Right-skewed, bounded below by 0. df=n−1. Sum of squared standard normal variables. Used for variance tests.

Question 3

Student's t-Distribution

Accepted Answer

Symmetric, bell-shaped, heavier tails than normal. Defined by degrees of freedom (df=n−1). Approaches normal as df increases.

Question 4

Multivariate Normal Distribution

Accepted Answer

Joint distribution of multiple normal random variables. Described by means, variances, and all pairwise correlations.

Question 5

Standardization (z-score)

Accepted Answer

z = (X − μ)/σ. Converts a normal variable to a standard normal variable for probability lookup.

Question 6

Standard Normal Distribution

Accepted Answer

Normal distribution with mean 0 and standard deviation 1. Denoted Z ~ N(0,1). Any normal variable can be standardized to Z.

Question 7

Normal Distribution

Accepted Answer

Symmetric, bell-shaped distribution defined by mean (μ) and variance (σ²). Mean=median=mode. Skewness=0.

Question 8

Binomial Distribution

Accepted Answer

Number of successes in n independent Bernoulli trials. P(X=x) = nCx × p^x × (1−p)^(n−x). E(X)=np, Var=np(1−p).

Question 9

Bernoulli Random Variable

Accepted Answer

Takes value 1 (success, prob p) or 0 (failure, prob 1−p). E(X)=p, Var(X)=p(1−p).

Question 10

Continuous Uniform Distribution

Accepted Answer

All outcomes in [a,b] equally likely. P(x₁≤X≤x₂) = (x₂−x₁)/(b−a). Mean=(a+b)/2. Var=(b−a)²/12.

Question 11

Discrete Uniform Distribution

Accepted Answer

All outcomes equally likely. P(X=x) = 1/n for each of n outcomes.

Question 12

Cumulative Distribution Function (CDF)

Accepted Answer

F(x) = P(X ≤ x). Ranges from 0 to 1, non-decreasing. P(a < X ≤ b) = F(b) − F(a).

Question 13

Probability Function p(x)

Accepted Answer

For discrete variables: gives P(X = x). Must satisfy 0 ≤ p(x) ≤ 1 and Σp(x) = 1.

Question 14

Probability Distribution

Accepted Answer

A function that specifies the probabilities of all possible outcomes of a random variable.

Question 15

Factorial

Accepted Answer

n! = n × (n−1) × ... × 1. The product of all positive integers up to n. 0! = 1 by definition.

Question 16

Permutation (nPr)

Accepted Answer

n!/(n−r)!. The number of ways to choose r objects from n when order matters.

Question 17

F-Distribution

Accepted Answer

Right-skewed, bounded below by 0. Has two df parameters. Ratio of two chi-square variables. Used for comparing two variances.

Question 18

Total Probability Rule

Accepted Answer

P(A) = Σ P(A|Si) × P(Si) for mutually exclusive, exhaustive scenarios Si. Computes unconditional probability from conditional probabilities.

Question 19

Independent Events

Accepted Answer

Two events where the occurrence of one does not affect the probability of the other. P(A|B) = P(A).

Question 20

Joint Probability

Accepted Answer

P(AB). The probability that both events A and B occur.

Question 21

Conditional Probability

Accepted Answer

P(A|B) = P(AB)/P(B). The probability of event A given that event B has occurred.

Question 22

A Priori Probability

Accepted Answer

Probability determined through logical reasoning about the problem rather than from observation.

Question 23

Subjective Probability

Accepted Answer

Probability based on personal or subjective judgment, without reference to specific data.

Question 24

Empirical Probability

Accepted Answer

Probability estimated from historical data as a relative frequency of occurrence.

Question 25

Exhaustive Events

Accepted Answer

A set of events that covers all possible outcomes. Their probabilities sum to 1.

Question 26

Mutually Exclusive Events

Accepted Answer

Events that cannot both occur at the same time. P(AB) = 0.

Question 27

Event

Accepted Answer

A specified set of outcomes of a random variable.

Question 28

Outcome

Accepted Answer

A possible value of a random variable.

Question 29

Random Variable

Accepted Answer

A quantity whose future outcomes are uncertain.

Question 30

Degrees of Freedom

Accepted Answer

The number of independent pieces of information in a dataset after accounting for estimated parameters. For sample variance: df = n − 1.

Question 31

Kurtosis

Accepted Answer

Measures tail thickness relative to a normal distribution. High kurtosis = heavy tails (more extreme outcomes).

Question 32

Null Hypothesis (H₀)

Accepted Answer

The default assumption being tested. Always contains the equality sign (=, ≤, or ≥). We either reject or fail to reject it.

Question 33

Economic Significance

Accepted Answer

Whether a statistically significant result is meaningful in practice after considering magnitude, transaction costs, risk, and out-of-sample persistence.

Question 34

Bonferroni Correction

Accepted Answer

When conducting m tests, use α/m as the significance level for each test to control the overall Type I error rate.

Question 35

Paired t-Test

Accepted Answer

A t-test for the mean difference of dependent (paired) samples. t = d̄/(s_d/√n), df = n−1.

Question 36

Pooled Variance

Accepted Answer

s²_p = [(n₁−1)s₁² + (n₂−1)s₂²]/(n₁+n₂−2). Weighted average of two sample variances used in independent samples t-test.

Question 37

Critical Value

Accepted Answer

The boundary value(s) of the test statistic that define the rejection region.

Question 38

One-Tailed Test

Accepted Answer

Tests whether a parameter is greater than (upper tail) or less than (lower tail) a hypothesized value.

Question 39

Two-Tailed Test

Accepted Answer

Tests H₀: μ = μ₀ vs. Hₐ: μ ≠ μ₀. Rejection region in both tails of the distribution.

Question 40

p-Value

Accepted Answer

The smallest significance level at which H₀ would be rejected. Reject H₀ if p-value ≤ α.

Question 41

Power of a Test

Accepted Answer

1 − β. The probability of correctly rejecting a false null hypothesis. Higher power = better test.

Question 42

Significance Level (α)

Accepted Answer

The probability of committing a Type I error — rejecting a true H₀. Common levels: 0.01, 0.05, 0.10.

Question 43

Type II Error

Accepted Answer

Failing to reject a false null hypothesis (false negative). Probability = β.

Question 44

Type I Error

Accepted Answer

Rejecting a true null hypothesis (false positive). Probability = α (significance level).

Question 45

Test Statistic

Accepted Answer

A value calculated from sample data that, compared to critical values, determines whether to reject H₀.

Question 46

Alternative Hypothesis (Hₐ)

Accepted Answer

What the researcher wants to prove. Contains ≠, >, or <. Accepted if H₀ is rejected.

Question 47

Skewness

Accepted Answer

Measures asymmetry of a distribution. Positive = long right tail. Negative = long left tail. Normal = 0.

Question 48

Time-Period Bias

Accepted Answer

Results depend on the specific time period chosen and may not generalize to other periods.

Question 49

Look-Ahead Bias

Accepted Answer

Using information in analysis that was not available at the time the decision would have been made.

Question 50

Survivorship Bias

Accepted Answer

A type of sample selection bias where failed or terminated entities are excluded, overstating average performance.

Question 51

Sample Selection Bias

Accepted Answer

Bias arising when the sample systematically excludes certain segments of the population.

Question 52

Data Snooping Bias

Accepted Answer

Finding spurious patterns by repeatedly analyzing the same dataset. Relationships found may not hold out-of-sample.

Question 53

Reliability Factor

Accepted Answer

The critical value (z or t) from the appropriate distribution used to construct a confidence interval.

Question 54

Standard Error

Accepted Answer

The standard deviation of the sampling distribution of a statistic. For the mean: σ/√n or s/√n.

Question 55

Confidence Interval

Accepted Answer

A range of values within which the true population parameter is expected to lie with a specified probability (confidence level).

Question 56

Consistent Estimator

Accepted Answer

An estimator that converges to the true parameter as sample size increases.

Question 57

Efficient Estimator

Accepted Answer

Among unbiased estimators, the one with the smallest variance.

Question 58

Unbiased Estimator

Accepted Answer

An estimator whose expected value equals the true population parameter.

Question 59

Point Estimate

Accepted Answer

A single number used to estimate an unknown population parameter.

Question 60

Parameter

Accepted Answer

A summary measure of a population (e.g., population mean μ).

CFA Level I - Quantitative Methods Glossary

Module 3: Probability Concepts

Module 4: Common Probability Distributions

Module 2: Organizing, Visualizing, and Describing Data

Module 6: Basics of Hypothesis Testing

Module 5: Sampling and Estimation

Module 1: Interest Rates, Present Value, and Future Value