Quantitative Methods & Statistics Flashcards

In a simple linear regression Y = α + βX + ε, the coefficient β represents:

Answer: The expected change in Y for a one-unit increase in X

β is the slope coefficient, representing the expected marginal change in Y for each additional unit of X, holding other factors constant.

An analyst wants to test whether the correlation between two variables is significantly different from zero. With n = 22 observations and r = 0.45, the appropriate test statistic is:

Answer: t = r√(n−2) / √(1−r²) with 20 df

The t-test for a sample correlation uses t = r√(n−2)/√(1−r²) with n−2 degrees of freedom.

Which of the following is an example of a priori probability?

Answer: Calculating the probability of rolling a 4 on a fair die as 1/6

A priori probability is derived from logical analysis of equally likely outcomes before any experiment, such as the 1/6 probability for each face of a fair die.

The standard error of the sample mean for a sample of n = 100 drawn from a population with σ = 20 is:

Answer: 2.0

Standard error = σ/√n = 20/√100 = 20/10 = 2.0.

Bayes' theorem is best used in CFA quantitative methods to:

Answer: Update prior probabilities given new information

Bayes' theorem provides a formal framework for revising (updating) prior probabilities when new evidence becomes available.

A lognormal distribution is most commonly used in finance to model:

Answer: Stock prices, because prices cannot be negative and tend to be right-skewed

Stock prices are modeled as lognormal because they are bounded at zero, positively skewed, and the continuously compounded returns are normally distributed.

Which of the following correctly defines the coefficient of variation (CV)?

Answer: CV = Standard Deviation / Mean

CV = σ/μ expresses risk per unit of expected return, enabling comparison of dispersion across datasets with different means.