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# Variance

### Variance of two jointly distributed Gaussian random variables

Let X and Y be two jointly distributed Gaussian random variables with means ηX and ηY and variance σ2X and σ2Y respectively. The correlation coefficient between X and Y is ρ. Let Z be a new random variable defined by Z = X-Y. Is Z Gaussian? What is the variance of Z?

### Joint characteristic function

Let X and Y be two jointly distributed Gaussian random variables. E[X]=ηX , E[Y]=ηY , var(X)=σ2X , var(Y)=σ2Y , and that the correlation coefficient between X and Y is r. What is the joint pdf of X and Y? What is the joint characteristic function of X and Y? Let Z = aX + bY , where a,b εR Is Z a Gaussian random varia

### Variance

True or False When we use separate-variance t-test for the difference between two independent population means U(1) AND u(2). We do not have to use a shared degree of freedom to find the value of t a/2.

### Gantt Chart and Network Analysis

1. Construct a Gantt chart for the following set of activities and indicate the project completion time:....see attached 19. Given the following network and activity time estimates, determine the expected time and variance for each activity and indicate the critical path:....see attached

### Multiple choice

66. Given the following data for Rene Company, compute (A) total manufacturing costs and (B) cost of goods manufactured: Direct materials used \$120,000 Beginning work in process \$20,000 Direct labor 100,000 Ending work in process 10,000 Manufacturing overhead 150,000 Beginning finished goods 25,000 Operating expens

2. Which one of the following responsibility centers is most likely to be the responsibility of a sales manager? a. Cost Center b. Profit Center c. Revenue Center d. Investment CenterPlease see the attached file.

### Maximum of standard deviation when mean is fixed

A set if numbers t1,...,tn has a mean of one and all numbers are non-negative. Show that the standard deviation could be as large as &#8730;(n-1).

### A simple mathematical statistics problem

Two statistically independent random variables X and Y have mean values 2 and 4 respectively, and 2nd order moment about the origin 8 and 25, respectively. Find the variance of the random variable W = 3X-Y

### Statistics: Difference between two causes of variation

Explain the difference between the two causes of variation, i.e. special or assignable cause and chance or common cause, and how they can be reduced.

### Multiple Choice Questions

1) If Larry gets a 70 on a physics test where the mean is 65 and the standard deviation is 5.8, where does he stand in relation to his classmates? (Points: 5) He is in the top 10%. He is in the top 20%. He is in the bottom 20%. He is in the bottom 10%. 2. Let's assume you have taken 100 samples of size 64 each from a

### mean, median, first quartile, and third quartile

Can anybody help me towards this one problem. It was thought to me differnt then it appears in the book. I was thought throught a lot of steps that is hard to remember, and then the books define them as short steps. I am soo confuse because the mean, range..... you follow different steps and is not like it was before because in

### The Expectation and Variance of a Random Variable

Let X be a random variable with the following probability distribution: Value x of X P(X=x) -10 0.05 0 0.30 10 0.40 20 0.10 30 0.15 Find the expectation E

### Calculating the Variance of Random Variables

Consider two random variables X and Y. Suppose that the variance of X is 10, that this of Y is 40, and that the covariance of X and Y is 15. What is the variance of the random variable 2X+Y? (Hint: Look at slide 45 of set 3 of lecture notes, or page 242 of text book) 80 90 110 140

### Summary Statistics and Student Religions

If you have a data set that consists of the frequency of various religions reported by students on your campus, indicate which of the following statistics you would use to describe your data and why. Mean, mode, median, range, standard deviation or variance?

The following data are for the Portland division: ROI 24% Stockholder's equity \$200,000 Net operating income \$288,000 Turnover 2 Sales ? Sales were: a.) \$750,000 b.) \$2,000,000 c.) \$3,846,154 d.) \$2,400,000 The controller of whitewater hospital estimates the amount of overhead costs that should be all

### Materials price variance..

The following standards have been established for a new raw material used in the production of product G13: Standard quantity of the material per unit of output 2.3 liters Standard price of the material \$1.90 per liter The following data pertain to a recent month's operations: Actual material purchased 5,100 li

### Accounting : Materials, Labor and Overhead

Inman Corporation manufactures a single product. The standard cost per unit of product is as follows. Direct materials - 2 pounds of plastic at \$5 per pound \$10 Direct labor - 2 hours at \$12 per hour 24 Variable manufacturing overhead 12 Fixed manufacturing overhead

### Accounting : Performance Reports and Flexible Budget Approach

The St. Lucia Blood Bank, a private charity partly supported by government grants, is located on the Caribbean island of St. Lucia. The Blood Bank has just finished its operations for September, which was a particularly busy month due to a powerful hurricane that hit neighboring islands causing many injuries. The hurricane large

### Finding central tendency measurements of some data sets.

1. Give two measures of variability.___________________ Which is the most reliable? 2. The distribution 0,2,2,3,13 has a mean of 4. What would the mean be if each score was multiplied by a constant of 2? 3. In the distribution 0,2,3,4,6, what is the percentile rank of the score 3? 4. Give three measures of central

### Statistics for a Set of Numbers

1. For the distribution 0,2,3,4,6, give the range. Is it more or less stable than the standard deviation? 2. When there are an even number of cases, simply average the two middle scores. The median of 0,6,9, and 12 is? 3. For the distribution 0,2,2,2,5,40, the skewness is positive or negative? 4. What is the mea

### Mathematical Statistics Objective type

1) Let Xl' X2,·.·, Xn, be a random sample from a Normally distributed population with mean 9 and variance 92 To find the Maximum Likelihood Estimator of B, which one of the followings is the likelihood function of 9 ? 2) Let Xl' X2, ... , Xn, be a random sample from a Normally distributed population with mean 9 and

### Project Management : Logisitics and Networks

Solve Problems 13-12, 13-13, & 13-16 13-12 Sid Davidson is the personnel director of Babson and Willcount, a company that specializes in consulting and research. One of the training programs that Sid is considering for the middle-level managers of Babson and Willcount is leadership training. Sid has listed a number of ac

Delta Company's flexible budget formula for overhead costs is \$100,000 per month fixed costs plus \$26.00 per unit variable costs. Standard volume is 5,000 units a month. Actual overhead coasts for June were \$280,000, and output was 6,000 units. Required: Determine for June a. Budgeted overhead at standard volume b. o

### P value for The Wall Street Journal

A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent): 4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6 At the .01 significance level, can we conclude that the 30-yea

### mean,median,sum of squared deviation,variance and standard deviation

For the following scores find the mean,median,sum of squared deviation,variance and standard deviation 2 2 0 5 1 4 1 3 0 0 1 4 4 0 1 4 3 4 2 1 0

### Cost accounting

These are varies cost accounting questions. Please help, I have no clue how these should be done. 1. A materials requisition slip showed that total materials requested were \$42,500 with \$1,500 of this amount consisting of indirect materials. What entry is made to record the transfer of materials from the storeroom? A) Work

### Methodology for Annual Percentage Return

Economy State Probability Stock A Stock B Good 0.5 40 20 Average 0.3 20 40 Bad 0.2 10 8 If one invested in Stock A, what would be the expected annual percentage return? Wh

### Direct material costs

Information on Rex Co.'s direct material costs for May follows: Actual quantity of direct materials purchased and used: 30,000 pounds Actual cost of direct materials: \$84,000 Unfavorable direct materials quantity variance: \$3,000 Standard quantity of direct materials allowed for May production: 29,000 pounds For the Mon

### Direct labor costs

Lion Company's direct labor costs for the month of January were as follow: Actual total direct labor hours 20,000 Standard total direct labor hours 21,000 Direct labor rate variance unfavorable \$3,000 Total direct labor cost \$126,000 What was Lion's direct labor efficiency variance?

### Descriptive Statistics: Variance

During a recent lengthy strike at Morell Manufacturing Company, management replaced striking assembly line workers with office workers. The assembly link workers were being paid \$18 per hour while the office workers rare only paid \$10 per house. What is the most likely effect on the labor variances in the first month of this str