Into to Quant Flashcards
(78 cards)
1
Q
What is probability
A
-The numerical likelihood that an event will occur
-A measure of uncertainty associated with events
-The chance of observing
2
Q
A sample space is
A
-A set of all possible experimental outcomes
3
Q
What is used to assign probabilities to sample space outcomes?
A
-Classical method
-Relative Frequency Method
-Subjective method
4
Q
Assigning 1/6 probability to each of the outcomes of a 6-sided dice is an example of
A
Classical method of assigning probabilities
5
Q
What is classical Method
A
equally likely sample space outcomes (dice, coin)
6
Q
What is a sample space
A
Set of all possible experimental outcomes
7
Q
What is the sum of all probabilities of the experimental outcome
A
1
8
Q
What is relative frequency
A
No reason to believe equality of
samples space outcomes (elections, preferences)
9
Q
What is subjective method
A
Use previous experience, judgment, or expertise
10
Q
Based on data from last year, I can say that the probability of you receiving an A in Statistical Analysis is 0.25. What method did I use to assign this
probability?
A
Subjective method
11
Q
The complement of an event is
A
All outcomes that are not the event
12
Q
Event B is the complement of event A. The probability of B is
A
b. 1 − p(A)
13
Q
The intersection of two events A and B is
A
All outcomes that occur in A and B
14
Q
The union of two events A and B is
A
All outcomes that occur in A or B
15
Q
When two circles intersect and its shaded in the middle
A
p(A ∩ B)
16
Q
When two circles intersect and its all shaded
A
d. p(A ∪ B)
17
Q
What does P(A ∩ B) mean
A
Intersection of events “and” - all sample space outcomes in A and B
18
Q
What is P(A U B)?
A
Union of events “or”
19
Q
What is mutually exclusive
A
A and B are mutually exclusive if they have no sample space outcomes in common - P(A∩B) = 0
20
Q
If A and B are not mutually exclusive, the union of the two will be
A
p(A) + p(B) − p(A ∩ B)
21
Q
If A and B are mutually exclusive, the union of the two will be
A
p(A) + p(B)
22
Q
A and B are mutually exclusive if
A
they have no sample space outcomes in common
23
Q
A and B are independent if
A
if the occurrence of A does not affect the occurrence of B
24
Q
The probability of an event A, given that the event B has occurred can be
denoted as
A
p(A|B)
25
Two events A and B are said to be independent if and only if:
p(A|B) = p(A)
26
What is the addition rule
where P(A∩B) is the joint probability of A and B both occurring
together
27
What is conditional probability
The probability of an event A, given that the event B has occurred, is
called the conditional probability of A given B
28
What is conditional probability denoted as
Denoted as P(A|B)
29
A quiz has 5 true-false questions. What are all possible ways one can answer
these questions i.e. what is the size of the sample space?
2^5
30
A quiz has 10 true-false questions. What are all possible ways one can
answer these questions i.e. what is the size of the sample space?
2^10
31
A quiz has 10 true-false questions. What are all possible ways one can
answer six of these questions correctly?
10!/
6!(10 - 6)!
32
A quiz has 10 true-false questions. What is the probability of answering
exactly six correct?
C10,6 /P2,10
33
What is a Continuous RV?
A continuous random variable is a random variable where the data can take infinitely many values.
Example: temperature of a cup of coffee or weights of students in this class
34
The Binomial distribution approximates to what distribution as the number of outcomes
increase?
Normal
35
The difference between discrete and continuous random variable is:
Discrete has countable number of values whereas continuous has infinitely many values
in a given interval
36
What are types of continuous probability distributions?
Continuous Uniform Distribution
Exponential Distribution
Normal Distribution
37
Example of Continuous Uniform Distibution
Suppose you arrive randomly at a bus stop every
morning, between 7:01 and 7:15.
The bus schedule is that it arrives every 10 minutes
(7:00, 7:10, 7:20)
What is the probability that you will wait more than
5 minutes?
38
Exponential Distribution and Example
Useful in describing the time or space between
events
Example:
Time between vehicle arrivals at a gate check
Time required to complete a questionnaire
Distance between major defects in a highway
Waiting line applications – time between customers
39
Suppose a customer spends of average of 10min in the bank. What
is the probability that any given customer would spend more than
5min upon arrival?
Exponential Distribution
40
Suppose, on an average, a customer spends 10min in the bank.
A customer arrives at 10AM. He waits in line till 10:10AM. Now, what
is the probability that he there longer than 15 min total?
Exponential Distribution
41
What is Forgetfulness Property of Exponential Distribution
The behavior during the next x-units of time is independent
upon the behavior during the past y-units of time. This is called the forgetfulness property.
42
What is the Relationship Between Poisson and Exponential
If number of arrivals per unit time is Poisson, then
time between arrival is exponential.
Suppose that average time no. of phone calls to a call
center is 2.5 calls per minute (Poisson), then the time
between phone calls has an exponential distribution
with average time = (2.5calls/60seconds) (=24
seconds)
43
The area of under the probability density curve is equal to:
Depends on the distribution
44
What are the two most used parameters used in normal distribution?
Standard Deviation and Mean
45
Approx what percentage of values (events) lie within 1 standard deviation away from the mean
in normal distribution?
68%
46
Approx what percentage of values (events) lie within 3 standard deviations away from the mean
in normal distribution?
99%
47
What is the standard normal distribution? It is Normal distribution with
μμ = 0 and σ = 1
48
What are these examples of: -Number of heads/tails from number of coin tosses
Number people arriving at Starbucks between 9:00 am and 10:00am
Amount of rain we’ll get tomorrow
Random variable
49
Rolling a dice is a
Discrete random variable
50
Number of people arriving at Starbucks between a given interval of time is
Discrete random variable
51
At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises
the temperature of the water that is discharged back into the ocean. The amount that the water
temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the
expected value of the temperature increase?
17.50
52
The Securities and Exchange Commission has determined that the number of companies listed
on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per
month. Find the probability that exactly 4 bankruptcies occur next month.
.1414
53
What is sampling
Sampling: The process of selecting a
number of elements for a study in such a way that the elements are representative of the population.
HWK: Selecting elements to research such that those elements are representative of the
population.
Sample: The elements selected for a study whose characteristics exemplify the population from which they were selected.
54
“Elements once chosen will not be selected again.” What kind of sampling is this?
Without replacement
55
What is sampling with replacement?
We place the element chosen on any particular selection back into the population
56
What is sampling without replacement?
We do not place the element chosen on a particular selection into the population. Element once chosen, will not be selected again - it is most common to sample without replacement
57
What are types of sampling
-Probability Sampling: Random Sampling; Systematic Sampling; Cluster Sampling; Stratified Sampling
-Convenience Sampling
-Judgment Sampling
-Voluntary-Response Sampling
58
What is Random Sampling
Select elements from a population such that every
element has an equal chance of being selected
Example: Select n random students from all students
at Pardee
59
“Select elements from a population such that every element has an equal chance of being
selected.” This is:
Random Sampling
60
Select the first 100 students from Pardee that you see. This is an example of:
Convenience Sampling
61
Sampling error is:
The difference between sample average and population average
62
Systematic Sampling
The list of elements is "counted off." That is,
every kth element is taken.
Example: Get a list of all students at Pardee and sample every 10th student
63
What is cluster sampling
Divide the total population into groups or
clusters
The students in each cluster are heterogeneous
The clusters should be mutually exclusive and
collectively exhaustive.
Select a random sample of the clusters.
Survey a random sample of the elements within
each selected group.
Example:
Divide the list of Pardee students by geographic
location (SM, DC, virtual).
Randomly select n students from each location.
64
What is the probability distribution of sample means if the population follows as a Poisson
distribution?
Normal
65
The variance of sampling distribution is/has
Inversely proportional to the sample size
66
Estimation is:
The process of making inferences from the sample
67
Confidence interval helps us to
Reasonably say that the interval contains the population parameter
68
Z value on the standard normal distribution is the:
Measurement of how many standard deviations is our calculated value away from a
given mean
b. Helps us find the probability of occurrence of our given value
c. Is calculated using standard deviation and mean
69
The 95 pct confidence interval is
xx̅± 1.96 σσxx
69
The t-distribution is different than normal distribution in that
It is more spread out
70
Homogeneity vs. Heterogeneity:
Stratified sampling focuses on creating homogeneous strata,
while cluster sampling deals with heterogeneous clusters
71
Allocation
Stratified sampling allocates sample
sizes based on strata proportions, while cluster sampling selects entire clusters.
72
Individual selection
Stratified sampling involves
random selection within strata, while cluster
sampling includes all individuals within selected clusters
73
A(n) ________ hypothesis is the statement that is being tested. It usually represents the
status quo, and it is not rejected unless there is convincing sample evidence that it is
false.
null
74
For a given hypothesis test, if we do not reject H0, and H0 is true,
no error has been committed.
75
The ________ hypothesis will be accepted only if there is convincing sample evidence
that it is true.
alternative
76
Using the critical value rule, if a two-sided null hypothesis is rejected for a single mean
at a given significance level, the corresponding one-sided null hypothesis (i.e., the same
sample size, the same standard deviation, and the same mean) will ________ be
rejected at the same significance level.
always
77
Using the critical value rule, if a two-sided null hypothesis is rejected for a single mean
at a given significance level, the corresponding one-sided null hypothesis (i.e., the same
sample size, the same standard deviation, and the same mean) will ________ be
rejected at the same significance level.
