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Determining Independent or Dependent Events

Independent Events (I) or Dependent Events (D) 1) A spinner is flicked three times, and each outcome is recorded. _____ 2) One thousand numbered raffle tickets are sold. Three different items are raffled off by randomly selecting three different raffle tickets. _____ 3) A paper bag holds 4 slips of paper that are numb

Setting up likelihood function and finding MLE

Consider the following data from 50 Bernoulli Trials Let theta be the probability of the observing a one for any single trial. a) Find the likelihood of any sequence of s trials containing y ones. b) If the prior on theta is uniform such that p(theta)=1, find an expression for the posterior distribution for theta after 10 t

Statistical Testing for an Out-of-Control Process

A statistical process analyst is responsible for assuring statistical control. In one process, a machine is supposed to drop 11.4 ounces of mints into a bag. (Assume that this process can be approximated by a normal distribution). The acceptable ranges for weights of the bags of mints are 11.25 ounces to 11.55 ounces, inclusive.

Binomial Probability Distributions - Sample Surveys

Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check

Steps on calculating the hospital's cost of capital

Assuming you are the financial manager of a for-profit hospital, what is the hospital's cost of capital assuming that the hospital has the following capital structure on its Statement of Financial Position (SFP; also known as a Balance Sheet): Long-Term Debt: $300M; current Yield to Maturity (YtM) of 6.5%, selling at par.

Linear Regression V1.0

The personnel director for a local manufacturing firm has received complaints from the employees in a certain shop regarding what they perceive to be inequities in the annual salary for employees who have similar performance ratings, years of service and relevant certifications. The personnel director believes that an employee'

Theoretical and Experimenatal Probability

Probability is an important topic, and students should be able to test theoretical computations against experimental data. Consider a deck of 52 cards with the following characteristics: 13 red cards, numbered 1 through 13 13 blue cards, numbered 1 through 13 13 green cards, numbered 1 through 13 13 black cards, numbered

Random variable expectation, Polya urn

I need help in two probability problems using R program. Thanks so much! 1. Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( X^X) when X has a U [0,1] distribution. Plot the value of the approximation as the sample size goes from 1 to 10,000. Use the Notebook feature in RStudio

Solving various questions on fundemantals of statistics

12. Which of the following numbers could be the probability of an event? 1.5 , 1/2 , 3/4 , 2/3 , 0 , -1/4 34. For some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, huntington's disease only requires on

Probability of a random sample

A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders. Suppose that this belief is correct. A random sample of 144 current stockholders is taken a. If random sample of 144 current stockholders is taken, what is th

Statistical Analysis of Simulation Results

" A company produces a product on a number of machines. Each machine generates between $200 and $400 of revenue per day according to the uniform probability distribution. When a machine breaks down, it must be repaired, and the repair time may take 1, 2, or 3 days to be completed according to the following probability di

Probability of Twin Births

Based upon statistical studies it has been found that 3.32% of all births in the United States will result in twins being born. If 17,300 births are selected at random what is the probability that: a) at most 600 of them will result in twins being born? b) between 525 and 550 of them (inclusive) will result in twins being born

Probability - Department Stores (J C Penney, Macy's, and Sears)

A mall has three department stores, JC Penney, Macy's, and Sears. A survey of 2,118 people exiting the mall found that 433 made a purchase at JC Penney, 412 made a purchase at Macy's, 638 made a purchase at Sears, 109 made a purchase at JC Penney and Macy's, 167 made a purchase at JC Penney and Sears, 213 of them made a purchase

Explaining Basic Logic of Probability Theory

If i take a selective quantitative data for an example like it takes me 15 minutes to get to work everyday for 10 days how can/would i describe it. What is my ability to explain the basic logic of probability theory & my ability to identify the meaning of independent and dependent events

Averages and Probability

The Wizard Tax Service is analyzing its operations during the month prior to the April 15 tax filing date. There is currently only one tax preparer at Wizard. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with and average time between arrivals of 12 minutes. When the tax

Using Binomial Probability Distribution

1 Pan Thai Restaurant offers 5% discount if the customer pays in cash instead of paying by a credit card. Past evidence indicates that 30% of all customers pay in cash. During a day period 120 customers buy gasoline at this station. (a) What is the probability that at least 50 customers pay in cash? (b) What is the

Applying the Probability Model

Please see attached files and use it to apply the questions if needed: 1) The definition of a probability model. Illustrate the two parts of the definition with an example selected from the worksheet. 2) Define the notion of independent events in a probability model. Using as your model the 36 element set of outcome

Probability: High Risk Apartments

In a local town, there are three separate apartment blocks, A, B and C. Block A contains 10 apartments, of which two contain "High Risk" inhabitants. Block B contains eight apartments, with three occupied by "High Risk" inhabitants, and Block C contains 12 apartments, with four "High Risk" apartments. Assume that an apartment

Probability Distribution: Learning Surveys

Learning is a lifetime activity. For some, it means learning from everyday experiences; for others, it means taking classes in a more traditional atmosphere. The percentage of people participating in organized learning situations during 2002 for each age group is reported here by NIACE. Age group:.........17-19...... 20-24.

Markov Chain and Steady State Probabilities

1. A production process contains a machine that deteriorates rapidly in both quantity and output under heavy usage, so it is inspected at the end of each day. Immediately after inspection the condition of the machine is noted and classified into one of four possible states: State 0: good as new 1: Operable - minimum deteri

Probability and Descriptive Statistics

Questions should be solved on excel file using excel functions. 1) Probabilities. A fair coin was tossed 3 times. Calculate the probabilities of the following 6 events. 1. Three heads were observed 2. Two heads were observes 3. One head were observed 4. At least two heads were observed 5. No more than two tails were o

Statistics and Probability Distribution

Please show all of the steps and processes you used to solve each of the problems 1. Would you suspect that the IDEA surveys sent to South students each term could be biased in the responses received? Why or why not? 2.Using the data set below, please calculate the: 12 16 12 10 20 10 10 - Mean = - Median =

Poisson Distribution: Birth-Death Process

The McDougal Sandwich Shop has two windows available for serving customers, who arrive at a Poisson rate of 40/hr. Service time is exponentially distributed with a mean of 2 min. Only one window is open as long as there are three or less customers in the shop. An identical server opens a second window when there are four or more

Algebraic Worksheet

Please see attachment 1. The triangles are similar. Find the value of a. (See attached for diagram) A. 12 B. 6 C. 16 D. 10 2. In a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed? A. 360 people B. 555 people C. 405 people D. 640 people 3. Find P(

Bayes Theorem - Decision Analysis - Type I & Type II Errors

See the attached file. Need step-by-step instructions on how to solve the following example problems: Decision Analysis The quality control manager in a chip manufacturing plant has to select one of two available quality control methods. The estimated error rates for the methods are presented below: (see attachment)

Moment generating function and poisson distribution

** Please see the attached file for the complete solution ** Shirley runs a real estate company. She counts the total number of flats that she sells everyday. Let X_t be the total number of flats she sells on day t (t=1,2,...,7), and let X be the total number of flats she sells for the week. Suppose X_t are independent and iden

Probability - Conditional Distribution, Law of total variance

A pollster wishes to obtain information on intended voting behavior in a two party system and samples a fixed number (n) of voters. Let X_1 ..., X_n denote the sequence of independent Bernoulli random variables representing voting intention, where E(X_l) = p, i = 1, ..., n (a) Suppose the number of voters n is fixed, compute

Probability and Statistical Methods

1. A manufacturing intraocular lens is in a process of verifying a polishing machine. The polisher will be accepted only if the percentage of polished lenses containing surface defects does not exceed 1.5%.They took a sample of 300 lenses and found 5 lenses that had surface defect. Formulate a test appropriate for verification o

Tree Diagram and Dice Tossing

Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Discuss the purpose of using such a visual in working out probability.