Practice Exam Questions
a) Calculate and interpret covariance given a joint probability
function
The joint probability function of two random variables X and Y,
denoted P(X,Y) gives the probability of joint occurrences of values of X
and Y. For example, P(3,2) is the probability that X=3 and Y=2.
Suppose that the joint probability function of the returns on BankCorp
stock (RA) and the returns on NewBank stock (R B has the simple
structure given below:
The expected return on BankCorp stock is 0.2(25%) + 0.5(12%) +
0.3(10%) = 14%
The expected return on NewBank stock is 0.2(20%) + 0.5(16%) +
0.3(10%) = 15%
b) Calculate and interpret an updated probability using Bayes’
formula
Bayes’ formula makes use of the total probability rule but reverses the
“given that” information. It uses the occurrence of the event to infer
the probability of the scenario generating it. It is sometimes called an
inverse probability. b) Identify the most appropriate method to solve a particular
counting problem, and solve counting problems using factorial,
combination, and permutation concepts
See page 470 for a summary of
this chapter.
Subjective Probability – a probability drawing on personal or subjective
judgment
Empirical Probability – the probability of an event estimated as a
relative frequency of occurrence
Priori Probability – based on logical analysis rather than on observation
or personal judgment
d) Define a probability distribution and distinguish between
discrete and continuous random variables and their probability
functions
Probability Distribution – specifies the probabilities of the possible
outcomes of a random variable
- ex. Uniform, binomial, normal and lognormal distributions Discrete Random Variable – can take on, at most, a countable number
of possible values
Continuous Random Variable – cannot count the outcomes
Probability Function – specifies the probability that the random
variable takes on a specific value
- P(X=x) is the probability that a random variable X
takes on the value x
For continuous random variables, the probability function is denoted
f(x) and called the probability density function. P(x) is between 0 and
1, and the sum of the probabilities p(x) over all values of X is 1.
e) Describe the set of possible outcomes of a specified discrete
random variable
A discrete random variable X can take on a limited number of
outcomes x1, x2, ..., xn (n possible outcomes), or a discrete random
variable Y can take on an unlimited number of outcomes y1, y2, ...
(without end).1 Because we can count all the possible outcomes of X
and Y (even if we go on forever in the case of Y), both X and Y satisfy
the definition of a discrete random variable. By contrast, we cannot
count the outcomes of a continuous random variable.
f) Interpret a cumulative distribution function
The cumulative distri

More
Less