A non-numerical observation, such as a person's political party, can not be a discrete variable.
False; Non-numerical observations can be discrete
The ratio of two ordinal values results in a quantitative data point.
False; Ordinal scale does not provide interval information
The correlation coefficient between two variables can only have values from -1 to 1.
True
Only two outcomes are possible for each trial in a Binomial experiment.
True
A joint probability is an example of a posterior probability.
False; Joint probability is probability of the intersection of two events
The second quartile point separates the second and third quartiles.
True
The z-value denotes the number of standard deviations a measure is from the mean of a distribution
True
Response time is an example of a discrete random variable.
False; response time is continuous
If you assign integer values to nominal data (such as investment portfolio 1 and 2), the data will then be
quantitative.
False
The covariance captures the linear relationship between two variables.
True
The joint probability of two events equals the probability of the intersection of the two events.
True
If P(A ∪ B) = P(A) - P(B), then events A and B are mutually exclusive events.
False; if P(A)+P(B)
A skewness of 1.0 implies that a distribution is symmetric.
False; symmetric will have skewness=o
A fund type can be an element.
True
According to Chebyshev's Theorem, at least 1 - 1/z2 of the data values in any distribution must be within
z standard deviations of the mean (for z > 1).
True
A posterior probability is a revision of a prior probability.
True
The correlation coefficient between two variables can only have values from -1 to 1.
True
The RAND function in Microsoft Excel provides uniformly distributed output.
True
A conditional probability equals the product of two marginal probabilities
False; Conditional = Joint/Marginal
A marginal probability of 2.0 suggests that an event is very likely to occur.
False; Probabilities must be less than or = to 1
business decisions are often on an analysis of uncertainties such as..
what are the
1. chances
2. likelihood
3. likely
4. odds
numerical measure of the likelihood that an event will occur
probability
probability provides a ?
better description of uncertainty than expressions such as chances are "pretty goods," "fair," so on
probability values are always signed on a scale from`
0 to 1
probability near 0
event is unlikely to occur
probability near 1
an event is almost certain to occur
prob of 0
impossible to occur
prob of 1
certain to occur
any process that generates well-defined outcomes
experiment
e.g. tossing a coin, rolling a die
set of all possible experimental outcomes
sample space
any one particular experimental outcome
*element of the sample space
sample point
two basic requirements of probability
1 probability values assigned to each experimental outcome (sample point) must be between 0 and 1
2. the sum of all of the experimental outcome probabilities must be1
when assumption of equally likely outcomes is used as abases for assigning probabilities
classical method
e.g. has n possible outcomes -> probability assigned to each experimental outcome = 1/n
because each of the n sample points is assigned a probability of 1/n -->
both requirements are satisfied
assigning different values to every probability
-if given frequency data
relative frequency method
most appropriate when one cannot realistically assume that the experimental outcomes are euqlly likely
-and when little relevant data are available
subjective method
expresses a person's degree of belief, making it personal
subjective probability
collection of sample points (experimental outcomes)
event
e.g.
experiment = roll a die
sample space = {1,2,3,4,5,6}
event A = getting even number when the die is rolled
P(A) = {2,4,6}
*if the experimental outcome or sample point where 2,4,6; the event A has occurred
sum of the probabilities of the sample points in the event
probability of an event
event consisting all sample points that are NOT in A
complement of event A
requirement of complement of event A
P(A) + P(Ac) = 1
solving for P(A)
P(A) = 1 - P(Ac)
P(Ac) = 1 - P(A)
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event containing all sample points belonging to A or B or BOTH
union of events A and B
denotation of union of events A and B
AUB
either A or B occurs
t least one of the two events occur
AUB
event containing the sample points belonging to BOTH A and B
intersection of events A and B
denotation of intersection of events A and B
AnB
used to commute probability of the union of two events
addition law
addition law=
P (A U B) = P(A) + P(B) - P(A n B )
two or more vents are said to be mutually exclusive if the events do not have any sample points in
common
mutually exclusive
mutually exclusive --> P(AnB) = 0
so the addition law became
P (A U B) = P(A) + P(B)
considering the probably of event A given the condition that event B has occured
conditional probability
(PA|B)
P(A|B)=
P(AnB) / P(B)
*P(B) cannot equal to 0
P(B|A)
P(AnB) / P(A)
*P(A) cannot equal to 0
frequency data arranged in a table
contingency table/crosstabulation
values giving the probability of the intersection of two events
joint probabilities
provides summary of the probability information of the intersection of two events
joint probabilities intersection
probabilities which are located in the margins of the joint probability table
marginal probabilities
P (B|M) is not equal to P(B)
dependent events
P (B|M) is equal to P(B)
independent events
P(B|A) = P(B)
P(A|B) = P(A)
independent events
used to find the probabilty of an intersection of two events
multiplication law