Question 1

Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

Accepted Answer

A)  Beta distribution 
B)  Bernoulli distribution 
C)  Poisson distribution 
D)  Binominal distribution 
A)  Beta distribution 
B)  Bernoulli distribution 
C)  Poisson distribution 
D)  Binominal distribution B

Question 2

Use the data given below to answer the following questions).
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. $\begin{array} { | c | c | c | } 
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Fernale } & \text { Arts } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Fernale } & \text { Arts } \
\hline 5 & \text { Fernale } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Fernale } & \text { Arts } \
\hline 10 & \text { Male } & \text { Arts } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Fernale } & \text { Science } \
\hline 13 & \text { Fernale } & \text { Math } \
\hline 14 & \text { Male } & \text { Arts } \
\hline 15 & \text { Fernale } & \text { Arts }\\hline 
\end{array}$
-Use the multiplication law of probability to compute the probability that the respondent is male and prefers Math.

Accepted Answer

A)  $\frac { 8 } { 75 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 3 } { 225 }$ 
D)  $\frac { 3 } { 15 }$ 
A)  $\frac { 8 } { 75 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 3 } { 225 }$ 
D)  $\frac { 3 } { 15 }$ D

Question 3

Use the data given below to answer the following questions).
On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula).
-Which of the following is true of normal distributions?

Accepted Answer

A)  The mean, median, and mode are all equal. 
B)  Its measure of skewness is always greater than 1. 
C)  The range of the random variable X is bounded. 
D)  Mathematical formulas make it easier to compute normal distributions. 
A)  The mean, median, and mode are all equal. 
B)  Its measure of skewness is always greater than 1. 
C)  The range of the random variable X is bounded. 
D)  Mathematical formulas make it easier to compute normal distributions. A

Question 4

Use the data given below to answer the following questions).
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. $\begin{array} { | c | c | c | } 
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Fernale } & \text { Arts } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Fernale } & \text { Arts } \
\hline 5 & \text { Fernale } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Fernale } & \text { Arts } \
\hline 10 & \text { Male } & \text { Arts } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Fernale } & \text { Science } \
\hline 13 & \text { Fernale } & \text { Math } \
\hline 14 & \text { Male } & \text { Arts } \
\hline 15 & \text { Fernale } & \text { Arts }\\hline 
\end{array}$
-Which of the following is a continuous random variable?

Accepted Answer

A)  the outcomes of rolling two dice 
B)  the time to complete a specific task 
C)  the number of new hires in a year 
D)  the number of hits on a Web site link 
A)  the outcomes of rolling two dice 
B)  the time to complete a specific task 
C)  the number of new hires in a year 
D)  the number of hits on a Web site link

Question 5

Which of the following is true about variance?

Accepted Answer

A)  It measures the uncertainty of a random variable. 
B)  Higher variance implies low uncertainty. 
C)  It is the square root of a random variable's standard deviation. 
D)  It is the weighted average of all possible outcomes. 
A)  It measures the uncertainty of a random variable. 
B)  Higher variance implies low uncertainty. 
C)  It is the square root of a random variable's standard deviation. 
D)  It is the weighted average of all possible outcomes.

Question 6

Use the data given below to answer the following questions).
On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula).
-Which of the following characterizes a continuous random variable for which all outcomes between some minimum and maximum value are equally likely?

Accepted Answer

A)  exponential distribution 
B)  uniform distribution 
C)  normal distribution 
D)  lognormal distribution 
A)  exponential distribution 
B)  uniform distribution 
C)  normal distribution 
D)  lognormal distribution

Question 7

Explain the similarity between the formulas for computing population mean and expected value of discrete random variable X.

Accepted Answer

For a discrete random variable X, the ex

Question 8

Use the data given below to answer the following questions).
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. $\begin{array} { | c | c | c | } 
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Fernale } & \text { Arts } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Fernale } & \text { Arts } \
\hline 5 & \text { Fernale } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Fernale } & \text { Arts } \
\hline 10 & \text { Male } & \text { Arts } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Fernale } & \text { Science } \
\hline 13 & \text { Fernale } & \text { Math } \
\hline 14 & \text { Male } & \text { Arts } \
\hline 15 & \text { Fernale } & \text { Arts }\\hline 
\end{array}$
-Identify the correct statement from the following.

Accepted Answer

A)  The events that a respondent is female and chooses Math are not independent. 
B)  All events are independent of each other. 
C)  The events that a respondent is male and chooses Science are not dependent. 
D)  The events that a respondent is female and that she chooses Science are independent. 
A)  The events that a respondent is female and chooses Math are not independent. 
B)  All events are independent of each other. 
C)  The events that a respondent is male and chooses Science are not dependent. 
D)  The events that a respondent is female and that she chooses Science are independent.

Question 9

The expected value and variance of the Poisson distribution are equal to λ.

Accepted Answer

A) True 
 B)False

Question 10

Use the data given below to answer the following questions).
On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula).
-The exponential distribution:

Accepted Answer

A)  has the density function f x) = e-λx , for x ≥ 0. 
B)  models the time between randomly occurring events. 
C)  has an expected value λ. 
D)  is described by the familiar bell-shaped curve. 
A)  has the density function f x) = e-λx , for x ≥ 0. 
B)  models the time between randomly occurring events. 
C)  has an expected value λ. 
D)  is described by the familiar bell-shaped curve.

Question 11

For a discrete random variable X, which of the following computes the expected value?

Accepted Answer

A)  $\sum f \left( x _ { i } \right)$ 
B)  $\sum _ { i = 1 } ^ { \infty } x _ { i } f \left( x _ { i } \right)$ 
C)  $\sum _ { i = 1 } ^ { \infty } x _ { i }$ 
D)  $\sum ^ { f ( x ) }$ 
A)  $\sum f \left( x _ { i } \right)$ 
B)  $\sum _ { i = 1 } ^ { \infty } x _ { i } f \left( x _ { i } \right)$ 
C)  $\sum _ { i = 1 } ^ { \infty } x _ { i }$ 
D)  $\sum ^ { f ( x ) }$

Question 12

Use the data given below to answer the following questions).
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. $\begin{array} { | c | c | c | } 
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Fernale } & \text { Arts } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Fernale } & \text { Arts } \
\hline 5 & \text { Fernale } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Fernale } & \text { Arts } \
\hline 10 & \text { Male } & \text { Arts } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Fernale } & \text { Science } \
\hline 13 & \text { Fernale } & \text { Math } \
\hline 14 & \text { Male } & \text { Arts } \
\hline 15 & \text { Fernale } & \text { Arts }\\hline 
\end{array}$
-Which of the following will hold true if events X and Y are independent?

Accepted Answer

A)  PX) = PY) × PX and Y) 
B)  PY) = PX|Y) 
C)  PX and Y) = [PX) + PY)] - PX or Y) 
D)  PX) = PX|Y) 
A)  PX) = PY) × PX and Y) 
B)  PY) = PX|Y) 
C)  PX and Y) = [PX) + PY)] - PX or Y) 
D)  PX) = PX|Y)

Question 13

Use the data given below to answer the following questions).
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. $\begin{array} { | c | c | c | } 
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Fernale } & \text { Arts } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Fernale } & \text { Arts } \
\hline 5 & \text { Fernale } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Fernale } & \text { Arts } \
\hline 10 & \text { Male } & \text { Arts } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Fernale } & \text { Science } \
\hline 13 & \text { Fernale } & \text { Math } \
\hline 14 & \text { Male } & \text { Arts } \
\hline 15 & \text { Fernale } & \text { Arts }\\hline 
\end{array}$
-What is the probability that a respondent prefers Science given that the respondent is female?

Accepted Answer

A)  $\frac { 1 } { 15 }$ 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 7 } { 15 }$ 
D)  4
7 
A)  $\frac { 1 } { 15 }$ 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 7 } { 15 }$ 
D)  4
7

Question 14

Use the data given below to answer the following questions).
On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula).
-What is the probability of 8 takers or less for Arts subjects in the coming year?

Accepted Answer

A)  0.00716 
B)  0.01260 
C)  0.03164 
D)  0.04744 
A)  0.00716 
B)  0.01260 
C)  0.03164 
D)  0.04744

Question 15

If PX|Y) = PX), it implies that event Y is dependent on event X.

Accepted Answer

A) True 
 B)False

Question 16

How can normal probabilities be computed using Excel? Given the cumulative probability, how can the value of the random variable be found?

Accepted Answer

The Excel 2010 function NORM.DIST(x, mea

Question 17

Use the data given below to answer the following questions).
At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. The spinners each have four colored spaces - red, yellow, blue, and green. Red = 1, Yellow = 2, Blue = 3, and Green = 4
-Compute the variance of the random variable that denotes the possible summed scores from the two spinners.

Accepted Answer

The variance, Var[X], of a dis

Question 18

Use the data given below to answer the following questions).
At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. The spinners each have four colored spaces - red, yellow, blue, and green. Red = 1, Yellow = 2, Blue = 3, and Green = 4
-Compute the expected value of the random variable that denotes the possible summed scores from the two spinners.

Accepted Answer

For a discrete random variable

Question 19

Which of the following is true about the classical definition of probability?

Accepted Answer

A)  It is based on judgment and experience. 
B)  If the process that generates the outcomes is known, probabilities can be deduced from theoretical arguments. 
C)  The probability that an outcome will occur is simply the relative frequency associated with that outcome. 
D)  It is based on observed data. 
A)  It is based on judgment and experience. 
B)  If the process that generates the outcomes is known, probabilities can be deduced from theoretical arguments. 
C)  The probability that an outcome will occur is simply the relative frequency associated with that outcome. 
D)  It is based on observed data.

Question 20

The Excel function NORM.DIST finds probabilities for the standard normal distribution.

Accepted Answer

A) True 
 B)False

Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

Use the data given below to answer the following questions). On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula). -Which of the following is true of normal distributions?

Which of the following is true about variance?

Explain the similarity between the formulas for computing population mean and expected value of discrete random variable X.

The expected value and variance of the Poisson distribution are equal to λ.

Use the data given below to answer the following questions). On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula). -The exponential distribution:

For a discrete random variable X, which of the following computes the expected value?

Use the data given below to answer the following questions). On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula). -What is the probability of 8 takers or less for Arts subjects in the coming year?

If PX|Y) = PX), it implies that event Y is dependent on event X.

How can normal probabilities be computed using Excel? Given the cumulative probability, how can the value of the random variable be found?

Which of the following is true about the classical definition of probability?

The Excel function NORM.DIST finds probabilities for the standard normal distribution.

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Exam 5: Probability Distributions and Data Modeling

Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

Use the data given below to answer the following questions). On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula). -Which of the following is true of normal distributions?

Which of the following is true about variance?

Explain the similarity between the formulas for computing population mean and expected value of discrete random variable X.

The expected value and variance of the Poisson distribution are equal to λ.

Use the data given below to answer the following questions). On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. Hint: Use Poisson distribution formula). -The exponential distribution:

For a discrete random variable X, which of the following computes the expected value?

If PX|Y) = PX), it implies that event Y is dependent on event X.

How can normal probabilities be computed using Excel? Given the cumulative probability, how can the value of the random variable be found?

Which of the following is true about the classical definition of probability?

The Excel function NORM.DIST finds probabilities for the standard normal distribution.

Introduction to Labour Market Economics

Database Analytics

Data Visualization

Descriptive Statistics

Sampling and Estimation

Statistical Inference

Trendlines and Regression Analysis

Forecasting Techniques

Introduction to Data Mining

Spreadsheet Modeling and Analysis

Simulation and Risk Analysis

Linear Optimization

Integer and Nonlinear Optimization Models

Optimization Analytics

Decision Analysis

Filters