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# Probability

### Forecasting model for soft drinks

The number of cans of soft drinks sold in a machine each week is recorded below from left to right, with oldest data to the left of the table.... see attached

### Operations Research

Embassy Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the textbook will be successful. If successful, a profit of \$750,000 will be realized. If the company decides to publish the textbook an

### Operations Research

Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semi-dry Riesli

### Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company's new fleet of jet aircraft and a discount service using smaller capacity commuter planes. a. If nothing is known about the probabilities of the chance outcomes, determine the recommended decision using the optimistic, conservative, and minimax regret approaches.

Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company's new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle

### Probabilities, Confidence Intervals and Binomial Random Variables

8.50 Refer to Exercise 8.25, vhere we reported on the results of Harris polls conducted in 1983 and 1992. The 1992 results summarized the responses of n ? 1251 individuals, whereas we assumed that the results for the 1983 poll involved n = 1250 respondents. The data are summarized in the accompanying table for your convenience.

### Probability Generating Functions & Offspring Generating Function

A1. (i) Let X be a random variable with probability mass function ( pmf ) ..... Determine the probability generating function of X. (ii) Suppose that the probability generating function of a random variable X is given by .... Determine the probability mass function of X. [5 marks] (Hint: You may use the formula: P1 ... A

### Description of Probabilities

A survey of MBA students obtained the following data on "student's first reason for application to the school in which they matriculated". Reason for Application Quality Cost Other Totals Full time 421 393 76 890 Part time 821 986 122 1929 Letting A be the event that a student

### Probabilities

A survey of MBA students obtained the following data on "student's first reason for application to the school in which they matriculated". Reason for Application Quality Cost Other Totals Full time 421 393 76 890 Part time 821 986 122 1929 I need to show if a student goes part

### Joint and Marginal Probability

Through a telephone survey, a low-interest bank credit card is offered to 400 households. The responses are as tabled. Income = \$40,000 Income > \$40,000 Accept offer 40 30 Reject offer 210

### Probability and Events for Centers of Disease Control

1. The following table, based on the data from the Centers for Disease Control, gives the number of new cases of the AIDS virus for men and women in the United States in 1998 by method of transmission. Method of Transmission Male Female Total Homosexual contact 8388

### Statistics : Sampling Distributions and Probabilities

Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the average annual Medicare spending per enrollee was \$3267; in 2003, the average annual Medicare spending per enrollee was \$6883 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to fu

### Statistics: Sampling Distribution and Probability Problems

The average annual cost of automobile insurance is \$687 (National Association of Insurance Commissioners, January 2003). Use this value as the population mean and assume that the population standard deviation is &#963; = \$230. Consider a sample of 45 automobile insurance policies. a. Show the sampling distribution of x where

### Statistics

Fifty percent of Americans believed the country was in a recession, even though technically had not shown two straight quarters of negative growth (Business Week, July 30, 2001). For a sample of 20 Americans, make the following calculations. a. Determine the probability that exactly 12 people believed the country was in a re

### Probability problem

3. A production line manufactures 1000 ohms resistors that must satisfy a 10% tolerance. a. If a resistance is adequately described by a Gaussian random variable for which mean = 1000; and standard deviation = 40;, what fraction of the resistance expected to be rejected? b. If a machine is not properly adjusted, the produc

### Statistics

In an article about investment growth, Money magazine reported that drug stocks show powerful long-term trends and offer investors unparalleled potential for strong and steady gains. The federal Health Care Financing Administration supports this conclusion through its forecast that annual prescription drug expenditures will reac

### Quantitative Methods

Hello Brainmass: Please answer the attached 60 Quantitative methods questions (some are t or f, some are multiple choice). This would be a great study guide for me.

### Moment Generating Function, Marginal and Conditional Distributions and Probability Density Functions

1. If the moment generating function ( mgf ) of X is (a) Find the mean of X. (b) Find the variance of X. (c) Find the pdf of X. 2. The joint probability mass function for random variables X and Y is: FXY (x, y) =(x + y)/32; x = 1, 2; y = 1, 2, 3, 4 (a) Show that fXY is a valid mass function. (b) Find the mar

### Statistics

The U.S. Bureau of Labor Statistics collected data on the occupations of workers 25 to 64 years old. The following table shows the number of male and female workers (in millions) in each occupation category (Statistical Abstract of the United States: 2002) (see chart in the attached file) a. Develop a joint probability tab

### Binomial Distributions and Z-Scores

1. A door to door salesperson believes that the probability of making a sale when a person is at home is 0.4 he visits 10 homes. When someone is at home find the probability of making a) exactly 7 sales b) more than 7 sales 2.For a binomial distribution with an n=200 and p=0.3 calculate the probability of obtaining between 50

### Kernel Density Estimator: Probability Density Function

Let K(u) be a probability density function symmetric about zero. Please show; integral f(x) dx =1.

### Describe three ways distributions can be represented (other than in a table that lists values for X and f(x))

Describe three ways distributions can be represented (other than in a table that lists values for X and f(x)).

### Probability Theory

Indicate whether the sentence or statement is true or false. T 1. Deterministic techniques assume that no uncertainty exists in model parameters. F 2. The probabilities of mutually exclusive events sum to zero. T 3. A joint probability is the probability that two or more events that are not mutually exclusiv

### Expectation and Variance: Rolling Dice and Flipping a Coin

1. (a) Roll a 6-sided die and then flip a coin the no. of times shown by the die. Letting Y be the no. of these flips coming up heads. What is E[X] and var(X)? (b) Repeat part a assuming first rolling two dice.

### Dice Probabilty: Convolving Probability Mass Functions (PMF)

There's 4 6-sided dice rolled independently. Set Y1 to be sum of the numbers on the first and second dice, Y2 to be sum of numbers on the third and fourth dice. Convolve PMFs of Y1 & Y2 to find the probability of the outcome of the 4 rolls summing to be 8.

### Simple Probability, Sample Spaces, Events

A couple has three children, assume the likelihood of a boy is the same as a girl: List sample space: {BBB,BBG,BGG,GGG} Event the children are grils: {GGG} Event the couple has one or more boy: {BBB,BBG,BGG} Probability all children are girls: 1/4 Probability the couple has at least one boy: 3/4 Probability the couple ha

### Eliminate parameter to find a cartesian equation of the curve

1) The manager of a fast food restaurant determines that the average time that her customers wait for service is 2.5 minutes. a) Find the probability that a customer has to wait for more than 4 mintues. b) Find the probability that a customer is served within the first 2 minutes. Now, this was all worked out, but some ste

### Problems on Probability, Probability Density Function Etc.

See attached and solve for 1, 3, 5 and 9 only. Give step by step solution with every minor detail.

### Equation of an Ellipse, Principal and Interest and Lotto Probabilities

Among the professionals you have interviewed for your article , were several state and federal government spokespersons who use linear equations in a variety of ways. 1. An employee of the National Parks service told you about a location in Washington , DC. It is a large grassy

### Applications of Parabolas and Hyperbolas: Real-Life Applications of Probability

One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wear

### Probability & Statistics : Mean, Median and Histograms

9. The price-to-earnings (PE) ratio of a stock is the ratio of a stock's most recent price per share to the stock's earnings per share (averaged over a 12-month period). Listed below are the PE ratios for 40 randomly selected securities traded on the New York Stock Exchange (NYSE) on Wednesday, August 24, 2005. Stock PE R