Chapter 13: Chi-Square Applications SHORT ANSWER 1. When samples of size n are drawn from a normal population‚ the chi-square distribution is the sampling distribution of = ____________________‚ where s2 and are the sample and population variances‚ respectively. ANS: PTS: 1 OBJ: Section 13.2 2. Find the chi-square value for each of the right-tail areas below‚ given that the degrees of freedom are 7: A) 0.95 ____________________ B) 0.01 ____________________ C) 0.025 ____________________
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2.3. The Chi-Square Distribution One of the most important special cases of the gamma distribution is the chi-square distribution because the sum of the squares of independent normal random variables with mean zero and standard deviation one has a chi-square distribution. This section collects some basic properties of chi-square random variables‚ all of which are well known; see Hogg and Tanis [6]. A random variable X has a chi-square distribution with n degrees of freedom if it is a gamma
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The Normal and Lognormal Distributions John Norstad j-norstad@northwestern.edu http://www.norstad.org February 2‚ 1999 Updated: November 3‚ 2011 Abstract The basic properties of the normal and lognormal distributions‚ with full proofs. We assume familiarity with elementary probability theory and with college-level calculus. 1 1 DEFINITIONS AND SUMMARY OF THE PROPOSITIONS 1 Definitions and Summary of the Propositions ∞ √ Proposition 1: −∞ 2 2 1 e−(x−µ) /2σ
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Weston Materials‚ Inc.‚ a national manufacturer of unattached garages‚ reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect? z(29) = (29-32)/2 = -3/2 z(34) = (34-32)/2 = 1 z(32) = 0 P(32 < x < 34) = P(0< z < 1) = 0.34 b. What percent of the
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X-bar Definition 1 x xi n i 1 Probability and statistics - Karol Flisikowski n Sampling Distribution of x-bar How does x-bar behave? To study the behavior‚ imagine taking many random samples of size n‚ and computing an x-bar for each of the samples. Then we plot this set of x-bars with a histogram. Probability and statistics - Karol Flisikowski Sampling Distribution of x-bar Probability and statistics - Karol Flisikowski Central Limit Theorem The key to the
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AMA470 Midterm exam March 5‚ 2010 Please show full working out in order to obtain full marks. 1. Suppose that: • The number of claims per exposure period follows a Poisson distribution with mean λ = 110. • The size of each claim follows a lognormal distribution with parameters µ and σ 2 = 4. • The number of claims and claim sizes are independent. (a) Give two conditions for full credibility that can be completely determined by the information above. Make sure to define all terms in your definition
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Probability Distribution Essay Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH‚ HT‚ TH‚ and TT. Now‚ let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0‚ 1‚ or 2‚ so it is a discrete random variable Binomial Probability Function: it is a discrete distribution. The distribution is done when the results are not ranged along a wide range‚ but are
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HVDC Moyle‚ the Isle of Man and France HVDC Cross-Channel. The electrical energy generated for the National grid needs to be moved around all parts of the country to supply the demand. There are two methods available for the transmission and distribution of electric power and these are: * Underground Insulated Cables * Overhead Cables (Bare Conductors Suspended at a Safe Height Above Ground) The overhead lines are generally used for high-voltage long distance transmission‚ because the
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skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately
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The Poisson probability distribution‚ named after the French mathematician Siméon-Denis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson
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