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# Variance

### ARMA Process

Use the equation for the Gaussian likelihood for an ARMA process (5.2.9 attached) to show that for n > p, the likelihood of the observations {X1, .... Xn} of the causal AR(p) process is ... (5.9 attached).

### Helix Company Material labor overhead variances P8-24A

Using the excel template provided, construct the material, labor and variable overhead variances for Helix Company for April given the robes actual produced, yards of fabric used and so forth. See attached.

### Cost and schedule variance calculations

The data below describes a housing refurbishment project that a small business contractor worked on: Activity Duration Predecessors Task Budget A 3 Days --- \$4,920 B 6 Days --- \$7,680 C

### Compute Var(k1), Var(k2), and Cov(k1, k2)

Consider 2 stocks with return K1 and K2 given by Scenario Probability Return k1 Return K2 w1 0.5 10% 7% w2 0.5 12% 10% Compute Var(k1), Var(k2), and Cov(k1, k2). Note Ki is the log returns.

### Predicting Annual Precipitation.

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

### Calculations with unbiased estimators

Please see the attached file for full problem. a) Using the results for the gamma distribution, show that s^2 is an unbiased estimator of sigma^2. Also state its variance. b) Consider a statistic of the form T_k = ks^2, for some constant k. Find expressions for the bias and variance of T_k as an estimator of sigma^2. Hene,

### Portfolio Optimization Problem

Create an Excel optimization file with good modeling techniques. Using Solver and Solver Table. Not sure how to get started on this problem any help would be appreciated. Thank you. Here is the problemt: Portfolio Optimization Problem The annual returns for three companies over the last 12 years are given below, wh

### Descriptive Statistics for Taking the Subway to Work in NYC

Randomly selected 50 people from New York City were asked if they use a subway to get to the work place. 40 said "Yes". Based on this sample data was made a statement that for the whole population of New York City residence 80% take subway to get to the work place. Does this statement represent descriptive or inferential stati

### Cannondale variable expense variance; sell to breakeven

Suppose that the master budget for Cannondale shows total variable expenses of \$10,000. The budget was based on production of 5,000 units. Cannondale sells all units it produces. Budgeted net income was \$5,000. Actual production and sales was 4,500. What is the variable expense variance? \$5,000 \$4,500 \$500 \$1,000 2. Ca

### Compute the Expected Return and Standard Deviation

Based on the following information, compute the expected return and standard deviation for Stock A and Stock B. Rate of Return if State Occurs State of Economy Probability of State Stock A Stock B of Economy

### Variance of total repair costs in 2012 for fixing cars after accidents

The cost of fixing car after an accident can be broken into 2 components: parts X, and labor Y. For 2010, you are given that E(x)=1,250, E(X^2)=1,800,000 and E(Y)=350, E(Y^2)=250,000. Var(X+Y)=875,000 For 2011 the cost of parts will be 4% lower uniformly while labor will be 6% higher uniformly. Calculate the variance of tota

### Materials price variance

Expireall Corporation is in the finishing business. The following data took place during September: Number of units produced 500 units Material purchased 1,500 feet material used in production 1,050 Cost per foot of material per purchase \$5.00 The standard cost card indicates that 2.0 fe

### Labor Rate & Efficiency Variance

Florr Shine Corporation: Selected data for April are given below: Number of units produced 1,000 units Number of actual direct labor hours worked 1,500 hours Total actual direct labor costs 16,500 The standard cost card indicates that 1.5 hours at \$10.00 of di

### Corporate Finance

(Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here. a. Calculate the expected returns on the stock market and on Chicago Gear stock. b. What is Chicago Gear's beta? c. What is Chicago Gear's required return according to the CAPM?

### Statistics: Mean, Variance and Random Variable

Given the values below: 1. mu = 2 and (sigma^2) = 0.5 a) Find the mean of the random variable: Z = 3x - 2 b) Find the variance of the discrete random variable above. 2. Given: Z = 2x + 3 a) If the mean of X = 4, what is the mean of Z? b) If the variance of x = 0.8, Find (sigma^2) of z

### Finding the Mean and Variance of Random Variables

Dealers profit is a random variable, x, having the probability density shown below. f(x) = 2(1 - x) 0 < x < 1 0 elsewhere a) Find the mean of x b) Find the variance of x

### Statistics

The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. Admissions Probability 1,070 0.3 1,300 0.1 1,580 0.6 -------------------------------------------------------------------------------- (1) Wha

### Management science - CPM/PERT

PM Computers is an international manufacturer of computer equipment and software. It is going to introduce a number of new products in the coming year, and it wants to develop marketing programs to accompany the product introductions. The marketing program includes the preparation of printed materials distributed directly by t

### CPM/PERT problem

The Center for Information Technology at State University has outgrown its office in Bates (B) Hall and is moving to Allen (A) Hall, which has more space. The move will take place during the 3-week break between the end of summer semester and the beginning of fall semester. Movers will be hired from the university's physical p

### Finance: Capital Budgeting - Risk Analysis

(Sequential Decisions)  The Haugen Yacht Company (HYC), a prominent sailboat builder in Florida, may design a new 30-foot sailboat based on the â??wingedâ? keels first introduced on the 12-meter yachts that raced for the Americaâ??s Cup.     First, HYC would have to invest \$10,000 at t=0 for the design and model tan

### Portfolio Diversifications: Allocations, portfolio variances, buy limit model

See attached file for clarity. Problem 1 Given: E(RÌ?A) = 10% Ï?2A = 0.25 E(RÌ?B) = 12% Ï?2B = 0.35 PAB = 0.56 Target Return = 11.5% Minimize: X2A(0.25) + X2B(0.35) + 2XAXB(0.56)(0.25)0.5(0.35)0.5 Subject to: 1 XA(10%) + XB(12%) = 11.5% E(RÌ?P) = 11.5%

### Comparison of Two Variances: Test Value & Degrees of Freedom

In comparing the two variances below, what is the test value and what are the degrees of freedom that should be used? Variance Number of values Sample 1 5 12 Sample 2 12 25 (Need test value and degrees of freedom).

### Flexible budgets and performance analysis

Palamino Jeep Tours operates jeep tours in the heart of the Colorado Rockies. The company bases its budgets on two measures of activity (i.e., cost drivers), namely guests and jeeps. One vehicle used in one tour on one day counts as a jeep. Each jeep has one tour guide. The company uses the following data in its budgeting:

### Mean, Median, Mode

Diana is costing her new employer \$1000 a month in benefits and salary. Her first months sales were disappointing. She offers piercings in 3 categories. Category I, II, III and cost \$35, \$55, \$75 for stainless steel and \$55, \$85, \$120 for gold. Diana sold five category I, two category II, and three category III in stainless stee

### Telemarketing: interaction of time and position, pairwise

See attached data file. A telemarketing firm has studied the effects of two factors on the response to its television advertisements. The first factor is the time of day at which the ad is run, while the second is the position of the ad within the hour. The data in Table attached, which were obtained by using a completely ran

### Personal Finance

1. Based on the data, determine the amount of total assets, total liabilities, and net worth. Liquid assets, \$3,670 Investment assets \$8,340 Current liabilities \$2,670 Household assets \$89,890 Long-term liabilities \$76,230 a. Total assets\$___________ b. Total liabilities \$________________ c. Net worth \$_________________

### Solve: Direct Labor Variances

XYZ Products uses a standard costing system to assist in the evaluation of operations. The company has had considerable employee difficulties in recent months, so much so that management had hired a new production supervisor. The new supervisor has been on the job for six months and has seemingly brought order to an otherwise c

### Mean, Autocorrelation, and Pdf

Let X(t) be a zero-mean wide-sense stationary Gaussian white noise process with autocorrelation function RXX(τ) = δ(τ). Suppose that X(t) is the input to a linear time-invariant system with an impulse response h(t) = 1[0,T](t) where T > 0. Let Y(t) be the output of the system, and assume that the input has been applied to the

### 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?