Question 1

The following table displays the joint probability distribution of X and Y.What is the covariance between the X and Y?

Accepted Answer

The answer of The following table displays the joint probability...

Question 2

A strong linear relationship is defined as a condition where the individual observation points are close to a straight line.

Accepted Answer

This is because a strong linear relationship is characterized by a tight cluster of data points that are aligned in a straight line. This means that the individual observation points are close to the line, indicating a high degree of correlation between the two variables being plotted.

Question 3

In a box of 20 chocolates,there are four chocolates with coconut filling.What is the probability of choosing four chocolates,one or more of which have coconut filling?

Accepted Answer

The answer of In a box of 20 chocolates,there are...

Question 4

Suppose you know that the number of complaints coming into a phone center averages 3 every ten minutes.Assume that the number of calls follows the Poisson distribution.What is the probability that there are exactly three calls during the next ten minutes?

Accepted Answer

The answer of Suppose you know that the number of...

Question 5

In a class of 18 students,there are 7 males and 11 females.A subcommittee of five students will be formed from this class.What is the probability that the subcommittee contains more males than females?

Accepted Answer

The answer of In a class of 18 students,there are...

Question 6

Thirty percent of all households have a DVD player.Suppose you select 20 houses at random.On average,how many houses of the twenty would you expect to have a DVD? What is the standard deviation of the number of houses with a DVD?

Accepted Answer

The answer of Thirty percent of all households have a...

Question 7

Consider the following probability distribution function.Compute the mean and standard deviation of X.

Accepted Answer

The answer of Consider the following probability distribution function.Compute the...

Question 8

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.
 
-What is P(2 < X < 5)?

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 9

Computation of marginal probabilities,means,and variances for jointly distributed random variables cannot be developed using a computer package.

Accepted Answer

Computation of marginal probabilities, means, and variances for jointly distributed random variables can be developed using a computer package, such as R, Python, or Matlab. These packages have built-in functions for calculating these quantities from the joint distribution.

Question 10

An auditor reviewing the invoices of a small company finds that there are errors in 1.5% of them.If the auditor looks at 500 invoices,what is the probability that he finds more than 3 invoices with errors? Use the Poisson approximation to the binomial distribution.

Accepted Answer

The answer of An auditor reviewing the invoices of a...

Question 11

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.
 
-What is P(X > 3)?

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 12

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a recent survey of 300 teenagers,62% of the teenagers indicated that they had been to a movie within the past month.75% of those teenagers who had seen a movie also had gone out to dinner in the past month,while only 64% of the teenagers who had not seen a movie had been out to dinner in the past month.Define the random variables as follows:
X = 1 if teenager had been to movie;X = 0 otherwise
Y = 1 if teenager had been out to dinner;Y = 0 otherwise
-Find the conditional probability function of X,given Y = 1.

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 13

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.
 
-What is P(X ≥ 2)?

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 14

Consider the following game.You choose a number from 1 to 6 and pay $1 to roll three dice.If your number is rolled on any of the dice,you get your dollar back and one dollar for each of the times your number came up.For instance,if your number comes up on two of the three dice,than you get a total of three dollars back.On average,how much would you expect to win at this game?

Accepted Answer

The answer of Consider the following game.You choose a number...

Question 15

In basketball,one of the possible penalties after a foul is called a free throw.The fouled player gets one shot at the basket from the foul line.If he misses this shot,he is awarded no points and the penalty is over.If he makes the shot,then he gets one point and gets to take another shot.If he makes the second shot he gets an additional point,and the ball is turned over to the other team.If he misses the second shot,the penalty is over.Suppose that the probability of making a shot is 80%,and the likelihood of making one shot is independent of the outcome of any other shot.What is the probability distribution function for the points from the penalty? On average,how many points would you expect to get from the penalty?

Accepted Answer

The answer of In basketball,one of the possible penalties after...

Question 16

Portfolio analysis and construction is conducted using probability distributions.

Accepted Answer

Portfolio analysis and construction involves assessing the risk and return of different investment assets and constructing a portfolio that optimizes the trade-off between risk and return. This process often involves using probability distributions to model the potential outcomes of different investment scenarios and to calculate the expected returns and risks associated with different portfolio compositions. Therefore, the statement is true.

Question 17

The following table lists the relative frequency distribution of the number of calls coming into a call center each hour.If each call takes five minutes to process,what is the mean and standard deviation of the number of minutes the operators are answering questions each hour?

Accepted Answer

The answer of The following table lists the relative frequency...

Question 18

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.
 
-What is P(X < 6)?

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a recent survey of 300 teenagers,62% of the teenagers indicated that they had been to a movie within the past month.75% of those teenagers who had seen a movie also had gone out to dinner in the past month,while only 64% of the teenagers who had not seen a movie had been out to dinner in the past month.Define the random variables as follows:
X = 1 if teenager had been to movie;X = 0 otherwise
Y = 1 if teenager had been out to dinner;Y = 0 otherwise
-Find and interpret the covariance between X and Y.

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 20

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a recent survey of 300 teenagers,62% of the teenagers indicated that they had been to a movie within the past month.75% of those teenagers who had seen a movie also had gone out to dinner in the past month,while only 64% of the teenagers who had not seen a movie had been out to dinner in the past month.Define the random variables as follows:
X = 1 if teenager had been to movie;X = 0 otherwise
Y = 1 if teenager had been out to dinner;Y = 0 otherwise
-Find the joint probability function of X and Y.

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Quiz 4: Discrete Random Variables and Probability Distributions

The following table displays the joint probability distribution of X and Y.What is the covariance between the X and Y?

A strong linear relationship is defined as a condition where the individual observation points are close to a straight line.

In a box of 20 chocolates,there are four chocolates with coconut filling.What is the probability of choosing four chocolates,one or more of which have coconut filling?

Suppose you know that the number of complaints coming into a phone center averages 3 every ten minutes.Assume that the number of calls follows the Poisson distribution.What is the probability that there are exactly three calls during the next ten minutes?

In a class of 18 students,there are 7 males and 11 females.A subcommittee of five students will be formed from this class.What is the probability that the subcommittee contains more males than females?

Thirty percent of all households have a DVD player.Suppose you select 20 houses at random.On average,how many houses of the twenty would you expect to have a DVD? What is the standard deviation of the number of houses with a DVD?

Consider the following probability distribution function.Compute the mean and standard deviation of X.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is P(2 < X < 5)?

Computation of marginal probabilities,means,and variances for jointly distributed random variables cannot be developed using a computer package.

An auditor reviewing the invoices of a small company finds that there are errors in 1.5% of them.If the auditor looks at 500 invoices,what is the probability that he finds more than 3 invoices with errors? Use the Poisson approximation to the binomial distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is P(X > 3)?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is P(X ≥ 2)?

Portfolio analysis and construction is conducted using probability distributions.

The following table lists the relative frequency distribution of the number of calls coming into a call center each hour.If each call takes five minutes to process,what is the mean and standard deviation of the number of minutes the operators are answering questions each hour?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is P(X < 6)?