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Probability

Real-life Applications of Hyperbolas and Parabolas

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 wearing

Prob & Stats - Sampling Distributions (6 questions)

1. Given the discrete uniform population f(x) = 1/3, x = 2, 4, 6, 0 elsewhere, Find the probability that a random sample of size 54, selected with replacement, will yield a sample mean greater than 4.1 but less than 4.4. Assume the means to be measured to the nearest tenth. 2. If the standard de

Math for Decision Making

1. The high school GPA of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories. GPA f(x) x < 2.0 .08 2.0 <= x < 2.5 .12 2.5 <= x < 3.0 .35 3.0 <= x < 3.5 .30 3.5 <= x ? a. Complete the table to make this a v

Problems in Math for decision making

1. There are two more assignments in a class before its end, and if you get an A on at least one of them, you will get an A for the semester. Your subjective assessment of your performance is: Event Probability A on paper and A on exam .25 A on paper only .10 A on exam only .30 A on neither .35 a. What

Probability : Sampling without Replacement

Consider a standard deck of playing cards. You randomly select a card from the deck and find that you have drawn a face card. If you don't replace the card, what is the probability that the next card you draw will be a king?

Gamma & Exponential Distribution/Log Nominal Distribution

1. In a certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with ? = 2 and ? = 3. If the daily capacity of that city is 9 million liters of water, what is the probability that on any given day the water supply is inadequate? 2. In a certain city, the daily consumpti

Uniform, Normal and Exponential Distributions and Conditional Probability

1. The length of time it takes to find a parking spot, during the summer terms on a campus, follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. The probability that a student, attending classes during the summer terms, will find a parking spot in less than 3 minutes is 2. Suppose t

Finance Math : Probability and Expected Value of a Payoff

Charles and Millie Jackson (a married couple in their 40's) have decided to invest a portion of their accumulated retirement "nest-egg" in a new business venture. It is an opportunity that Millie found while exploring one of her hobbies. Her idea is to embroider logos for small companies and organizations. They have already p

Continuous Probability Distributions

Normal Distribution: 1. Find the value of z if the area under a standard normal curve a) to the right of z is 0.3662 b) to the left of z is 0.1131 c) between 0 and z, with z > 0, is 0.4838 d) between -z and z, with z>0, is 0.9500 2. According to Chebyshev's theorem, the probability that any ra

Probability & Statistics

Some Discrete Probability Distributions - (Binomial & Multinomial Distributions/Hypergeometric Distribution/Negative Binomial & Geometric Distributions/Poisson Distribution) (See the attached file for full description). 1. In a certain city district the need for money to buy drugs is stated as the reason for 75% of all thef

You are given the choice of three doors. Behind one is a new car and the others hide a barnyard animal for you to keep. After you choose door number one, your host (Monty) opens door three to reveal a goat. He then asks you if you would like to switch to door two. Has the probability of success gone from 1/3 to 1/2 and then should you switch?

You are given the choice of three doors. Behind one is a new car and the others hide a barnyard animal for you to keep. After you choose door number one, your host (Monty) opens door three to reveal a goat. He then asks you if you would like to switch to door two. Has the probability of success gone from 1/3 to 1/2 and then s

Quantitative Methods of Business

Chez Paul is contemplating either opening another restaurant or expanding its existing location. The payoff table for these two decisions is: s1 s2 s3 New Restaurant -$80K $20K $160K Expand -$40K $20K $100K Paul has calculated the indifference probability for the lottery having a payoff of $160K with probability p and

Probability

Market Researchers, Inc. has been hired to perform a study to determine if the market for a new product will be good or poor. In similar studies performed in the past, whenever the market actually was good, the market research study indicated that it would be good for 85% of the time. On the other hand, whenever the market act

Probability Questions on Drawing Chips

An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip drawn. What is the probability of: a) a white chip on the first draw? b) a white chip on the first draw and a red on the second? c) two green chips drawn? d) a red chip on the second, given that a whit

Marginal Probability Density Function and Expected Values

Two stores A and B, which belong to (be same owner, are located in two different shopping centers. If X and Y, in thousands of dollars. are the profit made by each store in any week, the joint probability density function of these two random variables is given by .... a) Find the value of... b) Find the marginal probability d

Uniform Distribution and a 20-Sided Die

A 20-side (icosahedral) die has each face marked with a different integer from 1 through 20. Assuming that each face is equally likely to occur on a single roll, the outcome is a random variable X~DU(20) (DISCRETE UNIFORM DISTRIBUTION). a) If the die is rolled twice, find the pdf of the smallest value obtained, say Y. In t

Probability

Consider a seven-game world series between team A and B, where for each game P(A wins)=0.6 a) Find P(A wins series in x game) b) You hold a ticket for the seventh game. What is the probability that you will get to use it? .answer 0.2765 c) if P(A wins a game)=p, what value of p maximizes your chance in b)?answer p=1/2

The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway (following an exponential distribution). Planes arrive at the airport at the rate of 4 per hour (following a Poisson distribution). For purposes of this analysis, you can ignore the planes taking off.

The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway (following an exponential distribution). Planes arrive at the airport at the rate of 4 per hour (following a Poisson distribution). For pur

Probabilities and Uniform Distributions

You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 11:00. a) What is the probability that you will have to wait longer than 10 minutes? b) If at 10:20 the bus has not arrived, what is the probability that you will have to wait atleast an additional 10 m

Probability and Birthdays

From a set of n randomly chosen people, let Eij be the event that persons i and j have the same birthday. Assume that each person is equally likely to have any of the 365 days of the year as his or her birthday. Find a) P(E3,4|E1,2) b) P(E1,3|E1,2) c) P(E2,3|E1,2&#8745;E1,3) See attached file for full problem description.

Probability, Random Variables and Density Functions

1. A coin is biased so that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice. 2. An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, ¼, ¼, 1/6, and 1/6, respectively, that the a

Quantitative Methods : Random Numbers and Probability Distributions

I/ Explain why a decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available. II/ 1. ________________ is a technique for selecting numbers randomly from a probability distribution. 2. Random numbers of a mathematical proc

Mutually exclusive events: Example problem

Can a mutually exclusive events be independent at the same time? I know that Binomial distribution is not another representation of a discrete probability distribution, but an example. Can you give two other ways of representing a discrete probability distribution? Or Can a pair of events be both mutually exclusive and indepe