Study Session #3
Learning Outcome Statements
(Last revised 12/14/04)

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1. A. “Common Probability Distributions”
a) define and explain a probability distribution;
b) distinguish between and give examples of discrete and continuous random variables;
c) describe the set of possible outcomes of a specified random variable;
d) define a probability function, state its two key properties, and determine whether a given function
satisfies those properties;
e) define a probability density function;
f) define a cumulative distribution function and calculate probabilities for a random variable, given its
cumulative distribution function;
g) define a discrete uniform random variable and calculate probabilities, given a discrete uniform
distribution;
h) define a binomial random variable and calculate probabilities, given a binomial probability
distribution;
i) calculate the expected value and variance of a binomial random variable;
j) describe the continuous uniform distribution and calculate probabilities, given a continuous
uniform probability distribution;
k) explain the key properties of the normal distribution;
l) distinguish between a univariate and a multivariate distribution;
m) explain the role of correlation in the multivariate normal distribution;
n) construct and explain confidence intervals for a normally distributed random variable;
o) define the standard normal distribution and explain how to standardize a random variable;
p) calculate probabilities using the standard normal distribution;
q) define shortfall risk;
r) calculate the safety-first ratio and select an optimal portfolio using Roy’s safetyfirst criterion;
s) explain the relationship between the lognormal and normal distributions;
t) distinguish between discretely and continuously compounded rates of return;
u) calculate the continuously compounded rate of return, given a specific holding period return;
v) explain Monte Carlo simulation and historical simulation and describe their major applications and
limitations.
B. “Sampling and Estimation”
a) define simple random sampling;
b) define and interpret sampling error;
c) define a sampling distribution;
d) distinguish between simple random and stratified random sampling;
e) distinguish between time-series and cross-sectional data;
f) state the central limit theorem and describe its importance;
g) calculate and interpret the standard error of the sample mean;
h) distinguish between a point estimate and a confidence interval estimate of a population parameter;
i) identify and describe the desirable properties of an estimator;
j) describe the properties of Student’s t-distribution;
k) calculate and explain degrees of freedom;
l) calculate and interpret a confidence interval for a population mean, given a normal distribution
with 1) a known population variance or 2) an unknown population variance;
m) calculate and interpret a confidence interval for a population mean when the population variance
is unknown, given a large sample from any type of distribution;
n) discuss the issues regarding selection of the appropriate sample size;

o) discuss data-mining bias;
p) define and discuss sample selection bias, survivorship bias, look-ahead bias, and time-period bias.
C. “Hypothesis Testing”
a) define a hypothesis and describe the steps of hypothesis testing;
b) define and interpret the null hypothesis and alternative hypothesis;
c) distinguish between one-tailed and two-tailed tests of hypotheses;
d) discuss the choice of the null and alternative hypotheses;
e) define and interpret a test statistic;
f) define and interpret a Type I and a Type II error;
g) define and interpret a significance level and explain how significance levels are used in hypothesis
testing;
h) define the power of a test;
i) define and interpret a decision rule;
j) explain the relation between confidence intervals and hypothesis tests;
k) distinguish between a statistical decision and an economic decision;
l) identify the appropriate test statistic and interpret the results for a hypothesis test concerning the
population mean of a normally distributed population with 1) known or 2) unknown variance;
m) identify the appropriate test statistic and interpret the results for a hypothesis test concerning the
equality of the population means of two normally distributed populations, based on independent
random samples with 1) equal or 2) unequal assumed variances;
n) identify the appropriate test statistic and interpret the results for a hypothesis test concerning the
mean difference of two normally distributed populations (paired comparisons test);
o) identify the appropriate test statistic and interpret the results for a hypothesis test concerning the
variance of a normally distributed population;
p) identify the appropriate test statistic and interpret the results for a hypothesis test concerning the
equality of the variances of two normally distributed populations, based on two independent random
samples;
q) distinguish between parametric and nonparametric tests, and describe the situations in which the
use of nonparametric tests may be appropriate.
D. “Correlation and Regression”
a) calculate and interpret a sample covariance;
b) calculate and interpret a sample correlation coefficient;
c) formulate a test of the hypothesis that the population correlation coefficient equals zero and
determine whether the hypothesis is rejected at a given level of significance;
d) differentiate between the dependent and independent variables in a linear regression;
e) distinguish between the slope and the intercept terms in a regression equation;
f) explain the assumptions underlying linear regression;
g) calculate the standard error of estimate;
h) calculate and interpret the coefficient of determination;
i) calculate a confidence interval for a regression coefficient;
j) identify the test statistic and interpret the results for a hypothesis test about a population value of a
regression coefficient;
k) interpret a regression coefficient;
l) calculate a predicted value for the dependent variable, given an estimated regression model and a
value for the independent variable;
m) calculate and interpret a confidence interval for the predicted value of a dependent variable;
n) describe the use of analysis of variance (ANOVA) in regression analysis;
o) define and interpret an F-statistic;
p) discuss the limitations of regression analysis.

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