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    Probability Theory

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    Probability Problem with Playing Cards

    A standard pack of 52 playing cards is shuffled thoroughly and then cut. The pack is then shuffled and cut for a second time. Within the pack, a 'picture' card is defined to be a card showing an ace, king, queen or jack (that is, not a card showing any of the numbers 2, 3,... , 10). ** Please see the attachment for the full

    Discrete Least Squares

    Suppose you are given the data points x = {x0,x1,x2,......xn} ^T and the function values f= {f0, f1,f2,........fn}^T, where xi > 0 for all i = 0,1,2,......n a) For some reason, you think that h(x)= a + b*x + c*e^(arccos(x)) + d*sin(cos(T23(x))), where T23(x) is the 23rd degree Chebyshev polynomial is a great model for the dat

    Statistic Questions on Samples

    W2A3 Sample questions 1. For a particular sample of 63 scores on a psychology exam, the following results were obtained. First quartile = 57 Third quartile = 72 Standard deviation = 9 Range = 52 Mean = 72 Median = 68 Mode = 70 Midrange = 57 Answer each of the following: I. What score was earned by more stude

    Using Chebyshev's Theorem and Other Statistic Rules

    1. I. Use Chebyshev's theorem to find what percent of the values will fall between 162 and 292 for a data set with a mean of 227 and standard deviation of 13. II. Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data set with a mean of 246 and standard deviation of 16. 2. Nine coll

    Solving Probability Theory Questions

    Grindit & Floggit Ltd. make customized Widgets at a cost of $150 per unit of which 3% (on average) happen to be out of tolerance. Up to 115 Widgets can be produces in one continuous run whose set up incurs an additional cost of $10 000. Since manufacturing runs are set to produce one of many variants of Widget, Grindit & Floggit

    Measurements

    7 6 9 11 8 9 11 9 10 8 7 7 5 9 10 7 7 7 7 9 12 10 10 8 6 a. compute x (with line over), s^2, and s for this sample b. count the number of measurements in the intervals x (with line over) + and - s, x (with line over) + and - 2s, x (with line over) + and - 3s. Express each count as a percent

    Chebyshev's Theorem vs. Empirical Rule

    In the following example, why would Chebyshev's Theorem be used instead of the Empirical Rule? The Empirical Rule is a rule in statistics that says for a normal distribution, most of all of the data will land between three standardized yet different deviations from their mean. What the empirical rule does is it displays that

    Statistics (The Empirical Rule vs. Chebyshev's Theorem)

    How does the Empirical Rule work and how does it relate to the bell curve as illustrated in Figure 3.14 (a)? Then, explain Chebyshev's Theorem and how it is different from the Empirical Rule. Give a specific example of a population with which the Empirical Rule might be most effective and one with which Chebyshev's Theorem might

    compute and interpret the range, and the mean deviation

    Using the age of people compute and interpret the range, the mean deviation, the variance, and the standard deviation of the ungrouped age data. 2. Group the data into classes with five-year class widths, compute and interpret the range, the variance, and the standard deviation of grouped data. 3. Explain the characteristics

    Active filter types

    a) What is an active filter? What are its types? b) Derive the magnitude and the phase of the system gain of the low pass active filter with a pass-band gain Apb = 10 dB, RF = 10 kOhm and Rs = 1.1 kOhm. c) Plot the magnitude and phase frequency response curve for the low-pass active filter of (b).

    Chebyshev's Inequality

    Household income does not tend to follow a normal distribution in a particular state, yet average income is approximately $45,000/year in this state, with a standard deviation of about $9000. At least what percentage of household incomes in this state is likely to be between $18,000 to $72,000/year? Show your work as to how this

    Statistics Problem: Probability theory for BreatheCorp battery life

    See attached file for data and proper format. Problem Set 2 BreatheCorp manufactures two types of Portable Oxygen Concentrator Batteries: lithium ion and NiMH. 56% of the batteries they produce are lithium ion. They offer a 5,000 hour warranty on each of the batteries they sell, and 93% of all

    Statistical Analysis and Probability Sample Questions

    1. For a particular sample of 80 scores on a psychology exam, the following results were obtained: First quartile = 59 Third quartile = 90 Standard deviation = 10 Range = 57 Mean = 75 Median = 74 Mode = 41 Midrange = 69 Answer each of the following: I. What score was earned by more students than any other scor

    Chebyshev's Theorem for a Sample of Scores on a Psychology Exam

    For a particular sample of 77 scores on a psychology exam, the following results were obtained. First quartile = 44 Third quartile = 71 Standard deviation = 6 Range = 45 Mean = 64 Median = 57 Mode = 92 Midrange = 60 I. What score was earned by more students than any other score? Why? II. What was the highest score

    Statistics Theory True-or-False Questions

    True or False? 1. Statistics is a tool for turning data into information for making decisions. 2. Counting and categorizing are basic forms of statistics. 3. The mean and the median are essentially the same measures and are interchangeable. 4. Samples with the same means always have the same standard deviations. 5. The c

    Probability Theory

    1. There are two events A and B, both with nonzero probabilities. If the occurrence of B makes occurrence of A more likely, is it ALWAYS true that the occurrence of A also makes occurrence of B more likely? (hint: "B makes occurrence of A more likely" can be represented as "P(A│B) > P(A)") 2. A parking lot consists o

    Price of Gas, Hours of Student Study and UPS Box Weights

    See the attached file for the full problems. 1. NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is $1.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, WI, area revealed that the mean price was $1.52 per gallon and that the

    Probability Theory

    Given the Probability Axioms: Nonnegativity: P(A)  0 for every event A Additivity: if all Ai are disjoint, then: P(A1  A2 ...) = P(A1) + P(A2) + ... Normalization: P() = 1 1. Let A and B be independent events with AC denoting the complement of A. Prove that AC is independent of B

    Chebyshev's Theorem: Example Problem

    1. The lengths of pins produced by a machine follow a normal distribution with mean 2.54 cm and standard deviation 0.04 cm. A pin is rejected if its length is less than 2.44 cm or more than 2.60 cm. Find the percentage of pins that are accepted. 2. If it is decided that 2.5% of the pins are to be rejected because they are

    Probability Theory

    In a sample of 1,000 representing a survey from the entire population, 650 people were from Laketown, and the rest of the people were from River City. Out of the sample, 19 people had some form of cancer. Thirteen of these people were from Laketown. Are the events of living in Laketown and having some sort of cancer independe

    Refer to the Baseball 2005 data, which reports information

    Refer to the Baseball 2005 data, which reports information on the 30 major league teams for the 2005 baseball season. a. Select the variable team salary and find the mean, median, and the standard deviation. b. Select the variable that refers to the age the stadium was built. (Hint: Subtract the year in which the stadium was b

    Chebyshev's theorem

    The mean elevation of the 75 highest mountains in the United States is 15000 feet with standard deviation 1390. Whats the interval containing at least 75 percent and 89 percent of these elevations?

    Basic Statistics

    Part I T/F and Multiple Choice Questions 1. Each set of data has four quartiles; they divide the ranked data into four equal quarters. _____ (T/F) 2. For any distribution, the sum of the deviations from the mean equals zero. _____ (T/F) 3. In a data set, the mode will always be unique. _____ (T/F) 4. The mean, m

    Probability Theory with Coins, Dice and Cards

    1. Suppose you have 2 nickels, 3 dimes, and 8 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that a. You will draw a dime? b. You will draw a nickel? c. You will draw a quarter? 2. You are rolling a pair of dice, one red and one green. What is the probability of the

    Probability and Statistics

    Evaluate the permutation. 1) P( 9, 5) 1) _______ A) 9 B) 1 C) 504 D) 15,120 A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 2) All cherry 2) _______ A) .7272 B) .3636 C) .1091 D) .1212 In a ce

    Discussion Question

    Part A: What is dispersion? Briefly name five measures of dispersion. Describe the characteristics of the standard deviation. Explain! Part B: Briefly describe to what kind of data does Chebyshev's Theorem apply? To what kind of data does Empirical Rule apply? Explain.

    Mean, Median, Mode, Distributions and Standard Deviations

    1) Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for customers at the bank. Here are the waiting times (in minutes): 11, 21, 17, 9, 12, 23, 7, 5. A) What is the median of