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    Probability

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    Expectation and variance: sample solution

    Let be a random variable with the following probability distribution: Value Value x of X P(X=x) 4 0.30 5 0.05 6 0.20 7 0.30 8 0.10 9 0.05 Find the expectation E(X) and variance of VAR(X) of X

    Four Poisson Distribution Problems

    See attached file for clarity. #3. Assume that the number of uninspected cars caught at a state police checkpoint is Poisson distributed with average 2.1 per hour. (a) What is the average number of cars caught in t hours? (b) What are P(no cars caught in 14 hours? (c) P(at least 3 in 1.5 hours); (d) P(at least 1 car caught w

    Outcomes & Event Probability for Genders of Children

    Outcomes and event probability Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The outcomes are listed in the table below. Note that each outcom

    Probability of intersection or union: Age & Marital status

    Probability of intersection or union: Word problems Suppose that 51% of the women who gave birth at a certain hospital last year were over 30 years old, and that 39% were unmarried. If 63% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried

    Statistics: dice, marbles, survey, cards, smoker, tourist, participants

    Two sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 5? A bag contains 2 red marbles, 3 blue marbles and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? A case consists of 41 women and 74 men. If a student is rando

    Probability of intersection or union: pizza containing both

    Probability of intersection or union: At a certain pizza parlor, 45% of the customer's order a pizza containing onions, 38% of the customer's order a pizza containing sausage, and 79% order a pizza containing onions or sausage (or both). Find the probability that a customer chosen at random will order a pizza containing both

    Die Rolling probability

    Die rolling An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute t

    Calculating the Probability of Choice

    Please help with the following problems. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm's public relations office. Their employer must choose two of them to attend a conference in Paris. To be fair, the choice will be made by drawing two names from a hat. (This is an SRS of size 2) a) Write down all the possibl

    Probability models

    In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. Give specific reason for your answer. a) Roll a die and record the count of spots on the up-face: P (1) = 0 P (2) = 1/6 P

    Problems Involving the Rules of Probability

    Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American at random. Define two events: A) = the person chosen is obese B) the person chosen is overweight, but not obese According to the National Cente

    Discrete probability model

    Choose a person aged 19 to 25 years at random and ask, "how many times have you worked out in the past?" Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get: Days 0 1 2 3 4 5 6 7 Probability 0.68 0.05 0.07 0.08 0.05 0.04 0.01 0.02

    Probability Distribution: Operating a TrolleyLine

    4.1 Among its various routes, a transit agency operates a trolley line. The line has a total of 18 trolley cars. Some of these cars are unavailable because they are being maintained or repaired. The probability distribution of Y = number of cars out of service on a randomly chosen day is given by the Excel spreadsheet in figu

    Probability: Vehicle Type

    Vehicle type Lower Class Middle Class Upper Class Total Toyota Sienna 3 53 71 127 Honda Odyssey 2 34 77 113 Dodge Grand Caravan 62 11 7 80 Total 67 98 155 320 A. If we select one person at random, what is the probability that person drives a Toyota Sienna? B. If we select one person at random, what is the p

    Probability - Geologist's Analysis of Grantie Specimen

    A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis. a. What is the PMF of the number of granite specimens selected for analysis? b. What is the probability that all specimens of one of the

    Statistics

    Problem 2 Acme Tires manufactures two types of tires: high performance tires and all weather tires. 45% of the tires they produce are high performance tires. They offer a 40,000 mile warrantee on each of the tires they sell, and 89% of all tires exceed 40,000 miles of tread life. Furthermore, 37% of all the tires sold are both

    Probability that lifeline electricity usage is exceeded

    A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer

    Probabilities with Possible States of Nature

    Suppose that you are given a decision situation with three possible state of nature: s1, s2, and s3. The prior probabilities are P(s1) =.1, P(s2) = .6, and P(s3) = .3. With sample information I, P(I|s1) =.15, P(I|s2) = .2, and P(I|s3) = .1. Compute P(s1|I) Compute P(s2|I) Compute P(s3|I)

    Computing binomial probabilities

    Consider a binomial experiment with 2 trials and p = .3. For the following questions, round to the nearest hundredth. Compute the probability of 1 success f(1) Compute f(0) Compute f(2) Find the probability of at least 1 success What is the expected value? What is the variance? What is the standard d

    Probability of failure with redundant systems in aircraft engines

    Modern aircraft engines are very reliable. One feature contributing to that reliability is the use of redundancy, where critical components are duplicated so that if one fails, the other will work. For example, single-engine aircraft now have two independent electrical systems so that if one electrical system fails, the other ca

    Expected premium cost of an insurance policy

    A bonding company want to insure a construction projects completion. If the project is cancelled due to the contractor's lack of performance, the bonding company will cover the entire expenses of $30,000, and it will pay only half of this amount if it is cancelled for any other reason. The bonding company assigns a probabi

    Failure of airplane alternators; bus riders with same birthday

    1. A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully. 2. How many riders would there have t

    Statistics: Calculate probabilities in contingency tables

    1. Refer to the contingency table below and calculate the following probabilities. Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000 a) P(S) b) P(W) c) P(S | W) d) P(S | B) e) P(S and