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Poisson Distribution and MVUE.

1. Let -- be a random sample from the Poisson distribution with pmf --. Find the MVUE of --- using the following three steps. a) Find the complete sufficient statistic Y_1 for --. b) Show that -- is an unbiased estimator of -- where I is the indicator function. c) Find the MVUE of -- by the conditional expectation e(T/Y_1).

Random variable with exponential distribution

Please see the attachment for the full problem description. 1. A single observation of a random variable having an exponential distribution with ---- If the null hypothesis is accepted if and only if the observed value of the random variable is less than 3. a) Find the probabilities of Type I and Type II errors. b) W

probability for telecommunication problem

You are assigned to be part of a team of three analysts of a global management consulting company where of the entire work force of analysts. 55% have had no experience in telecommunications, 32 have had limited experience (less than 5 years) and the rest have had extensive experience ( 5 years or more). You and two other an

Probability of White Blood Cell Count Per Blood in an Adult

Workers at a large toxic clean up project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then m= 7500 and o= 1750. A random sample of n=50 workers from the toxic cleanup site were giv

Pepsi: probabilities, sensitivity analysis, decision tree

Please construct the decision tree for the problem attached, insert the probabilities and values as given in the scenario (make sure to include in the tree the possibility that the one-month forecast is favourable or not), roll back the tree, and determine the course of action that PEPSI should take. Perform a sensitivity ana

Probability problems regarding Facebook

Facebook reports that 70% of their users are from outside the United States and that 50% of their users log onto the Facebook everyday. Suppose that 20% of their users are United States users who log on every day. 1. What percentage of Facebook users are from the United States? 2. What type of probability is the 20% mentione

Probabilities: Online Police Department, Excite Poll

3. The Online police department was asked by the mayor's office to estimate the cost of crime to citizens of Online. The police began their study with the crime of identity theft, taking a random sample of files (there is too much crime to calculate the statistics for all the crimes committed). They found the average dollar lo

Age Distribution in the United States: Question

The following table gives the approximate age distribution in the United States from the 2000 census. Age Population 19 & under 29% 20 - 34 21% 35 - 59 34% 60 - 84 15% 85 & over 1% a. Does the dat

Men's Average Weight Questions

Data from a National Health Survey show that men's average weight is normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds. a. If a man is chosen at random, what is the probability that his weight is greater than 180 pounds? b. If 100 men are randomly selected, what is the probability tha

Average Stock Prices for Companies

The average stock price for companies making up the s&p 500 is $30, and the standard deviation is $8.20. assume the stock prices are normally distributed. a. what is the probability a company will have a stock price of at least $40? b. what is the probability a company will have a stock price for no higher than $20? c. how

Probabilities Standard Normal Variables

1. Given that z is a standard normal variable, compute the following probabilities a. p(z less than or equal to -1.0) b. p(z is greater than or equal to 1) c. p( z is greater than or equal to - 1.5) d. p(-2.5 less than or equal to z) e. p(-3 < z is less than or equal to 0) f. p(-1.98 less than or equal to z less than or eq

Probability calculation based on Z score

Each day a manufacturing plant receives a large shipment of drums of Chemical ZX-900. These drums are supposed to have a mean fill of 50 gallons, while the fills have a standard deviation known to be .6 gallon. Suppose that the mean fill for the shipment is actually 50 gallons. If a random sample of 100 drums from the shipmen

find probability based on Joint Density Function

Looking to see how the answer is derived. Suppose that X and Y are independent each with exponential distribution with parameter = 3. Joint Density Function = 9(e^-3x)x(e^-3y) for x>0 and y>0. Find (a) P(X + 2Y <,= 2); (b) P(X + Y <,= 2); and (c) P(X - Y <,= 2). <,= represents less than, equal to.

Probability Distribution of Random Variables of X

The probability distribution for the random variable x is as follows x is 20 25 30 35 f(x) is .20 .15 .25 .40 a. Is this probability distribution valid? Explain. b. What is the probability that x=30? c. What is the probability that x is less than or equal to 25? d. What is the probability that x is greater than 30?

Find probability using z score

Suppose that the net interest margins for all U.S. banks are normally distrubuted with a mean of 4.15 percent and a standard deviation of .5 percent. 1. What is the probability that a randomly selected U.S.bank will have a net interest margin less than 4.40 percent?

discrete probability distribution and continuous probability

Give an example representing a discrete probability distribution and another example representing a continuous probability distribution. Explain why your choices are discrete and continuous. Please provide me an insightful analysis of the question is lengthy in response and include specific examples.

Word-process your solutions within this template.

Word-process your solutions within this template. Show all steps used in arriving at the final answers. Word-process formulas using Equation Editor and diagrams using Drawing Tool. Please see attachments.

total probability from Binomial Distribution

The GMAT scores of MBA students is assumed to be distributed normally with a mean of 530 and a standard deviation of 80. The GMAT scores of ten students are selected randomly. What is the probability that at least 7 of the 10 students have SAT scores in excess of 550?

Group 6 and Group 7 Statistics Questions

Please answer the questions listed below (see attachment for formatted questions): Group 6 Airlines sometimes overbook flights (that is, they sell more tickets than there are seats on the plane). Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable X as the number of ticketed pass


Fluctuation in the prices of precious metals such as gold have been empirically shown to be well approximated by a normal distribution when observed over short interval of time. In May 1995, the daily price of gold (1 troy ounce) was believed to have a mean of $383 and a standard deviation of $12. A broker, working under these a

T-Distributions with Excel Formulas

Please help with the following problem. For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. a.) To the right of 2.120. (Use 3 decimals.) __________ b.) To the left of 1.337. (Use 2 decimals.) __________ c.) To the left of -1.746. (Use 2 decimals.) __________ d.

Probability question with an OR statement

If two dice are thrown, what is the probability that the first die shows a 4 or that the total on the two dice is 8? So far in calculations: Event A = 4/36 Event B = 5/36 (4/36 + 5/36) - 1/36 = 8/36 or 2/9 which is not the correct answer.

Normal random variable

A drug company believes that the annual demand for a drug will follow a normal random variable with a mean of 900 pounds and a standard deviation of 60 pounds. If the company produces 1000 pounds of the drug, what is the chance (rounded to the nearest hundredth) that it will run out of the drug? Assume that the only way to meet

Probability Statistics Problem

Suppose that 1% of all people have a particular disease. A test for the disease is 99% accurate. This means that a person who test positive for the disease has a 99% chance of actually having the disease, while a person who test negative for the disease has a 99% chance of not having the disease. If a person tests positive fo

A roulette wheel contains the integers 1 through 36, 0, 00

A roulette wheel contains the integers 1 through 36, 0, 00. Suppose that you spin the wheel 6 times and that each time you bet on a single number. What is the probability (rounded to nearest 100th) that you win on at least one bet? Possible answers: 0.09, 0.11, 0.13, 0.15, none of the above.

Probability of defective versus non-defective balls

A batch of 100 Barbie dolls contains four (4) defective dolls. What is the probability that a sample of three (3) dolls from this batch will contain: a) No defective dolls. b) All defective dolls. c) At least one defective dolls. d) At least one non-defective doll.

Joint Probability Table

Health Insurance (Proportion of Population) Yes No Age 18 to 34 750 170 35 and older 950 130 a. Develop a joint probability table for these data and use the table to answer the remaining questions. b. What do the mar

Probability of Independent Events: Example Problem

Reggie Miller of the Indiana Pacers is the National Basketball Association's best career free throw shooter, making 89% of his shots. Assume that late in a basketball game, Reggie Miller is fouled and is awarded two shots. a. What is the probability that he will make both shots? b. What is the probability that he will make a

z value based probability problem...

When sampling is done for the proportion of defective items in a large shipment, where the population proportion is 0.18 and the sample size is 200, what is the probability that the sample proportion will be at least 0.20?

Probability and Life Expectancy

The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of that age. Determine the following using the table: a. To what age may a female of age 60 expect