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For best results, please make sure your browser is accepting cookies. The Devil on Trial: Witches, Anarchists, Atheists, Communists, and Terrorists in America's Courtrooms: Philip Margulies, Maxine Rosaler: Books - Amazon.ca Amazon.ca Try Prime Books Go Shop by Department EN Hello. Sign in Your Account Try List. The NOOK Book (eBook) of the Possessed by the Devil: Ireland's Mass Witchcraft Trial by Andrew Sneddon at Barnes & Noble. FREE Shipping on $25 or more! Barnes & Noble Spend $25, Get Free Shipping shopping bag count Bob Dylan Wins 2016 Nobel. Franz Kafka's other trial An allegory of the fallen man's predicament, or an expression of guilt at a tormented love affair? What Heller prizes in. Featuring five famous trials, this book examines the way our right to a fair trial can be threatened, when people are tempted to abandon their principles in the name of safety. Trials included are the Salem Witch Trials, the Haymarket Affair Trial, the Scopes the. Amazon.com: The Devil on Trial: Witches, Anarchists, Atheists, Communists, and Terrorists in America's Courtrooms (Junior Library Guild Selection) (0046442717175): Philip Margulies, Maxine Rosaler: Books. Every now and then civilization goes a bit awry with.
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Find the latest business news on Wall Street, jobs and the economy, the housing market, personal finance and money investments and much more on ABC News. The Binomial Distribution. Bernoulli Trials. Basic Theory. Definitions. Our random experiment is to perform a sequence of Bernoulli trials \(\bs. The common probability of success \( p = \P(X. In statistical terms, the first \(n\) trails \((X. The underlying distribution, the binomial distribution, is one of the most important in probability theory, and so deserves to be studied in considerable detail. As you will see, some of the results in this section have two or more proofs. In almost all cases, note that the proof from Bernoulli trials is the simplest and most elegant. For \( n \in \N \), the number of successes in the first \(n\) trials is the random variable. By the additive property of probability. From the binomial theorem. For selected values of the parameters, run the simulation 1. The binomial distribution is unimodal: For \( k \in \. This integer is a mode of the distribution. In the case that \(m = (n + 1) p\) is an integer between 1 and \(n\), there are two consecutive modes, at \(m - 1\) and \(m\). Now let \( F. Vary \( n \) and \( p \) and note the shape and location of the distribution/quantile function. For various values of the parameters, compute the median and the first and third quartiles. The binomial distribution function also has a nice relationship to the beta distribution function. The distribution function \( F! Substitution and simple integration shows that \( G. Bernoulli Trials An experiment in which a single action, such as flipping a coin, is repeated identically over and over. The possible results of the action are classified as 'success' or 'failure'. The binomial probability formula is used to find. In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, is the probability distribution of a random variable which takes the value 1 with success probability of p Definition 1: Suppose an experiment has the following characteristics: the experiment consists of n independent trials, each with two mutually exclusive outcomes (success and failure) for each trial the probability of success is p (and so the probability of failure is 1 – p. Any distribution may be represented in graphic form. Since the binomial distribution tells us the probability of r success out of n trials. Therefore place values of r along the horizontal axis and values of P(r) on the vertical axis. A histogram is an appropriate graph of a. What is a Binomial Experiment? A binomial experiment is an experiment where you have a fixed number of independent trials with only have two outcomes. For example, the outcome might involve a yes or no answer. If you toss a coin you might ask yourself “Will I. Binomial Distribution Cumulative Distribution Function Cumulative Distribution Function = Pr (X . This is the probability that the count of successful outcomes, X, equals any number between k and 0 for n trials. Specification Probability mass function In general, if the random variable X follows the binomial distribution with parameters n . The probability of getting exactly k successes in n trials is given by the probability mass function. Bernoulli Trials De nition ABernoulli trialis a random experiment in which there are only two possible outcomes - success and failure. 1 Tossing a coin and considering heads as success and tails as failure. 2 Checking items from a production line: success = not. D de Morgan's Laws de Morgan's Laws are identities involving logical operations: the negation of a conjunction is logically equivalent to the disjunction of the negations, and the negation of a disjunction is logically equivalent to the conjunction of the negations. Hence from the additive property of expected value. Hence from the additive property of variance for independent variables. Using the binomial theorem. Note that the graph of \(\var(Y. In particular the maximum value of the variance is \(n / 4\) when \(p = 1 / 2\), and the minimm value is 0 when \(p = 0\) or \(p = 1\). Of course, in the last two cases, \( Y. For selected values of the parameters, run the simulation 1. The probability generating function of \(Y. Recall also that the PGF of \(X. If \( X \) is a random variable and \( k \in \N \), then \( \E\left. The probability generating function provides an easy way to compute the factorial moments of the binomial distribution.\( \E\left. By simple calculus, \(P. Here are the first four, which will be needed below. The first four moments of \( Y. For each of the following values of \( n \), vary \( p \) from 0 to 1 and note the shape of the probability density function in light of the previous results on skewness.\( n = 1. For \( p \in (0, 1) \), the kurtosis of \( Y. This is related to the convergence of the binomial distribution to the normal, which we will discuss below. The Partial Sum Process. Several important properties of the random process \(\bs. Also \( U \) has the same distribution as \( \sum. Then \(U + V\) has the binomial distribution with parameters \(m + n\) and \(p\). Proof from Bernoulli trials: Let \( (X. Then \(U\) has the same distribution as \(Y. The binomial distribution with parameters \( k \in \N. In particular, \( U \) has PDF \( f^. Hence by independence, \( U + V \) has PGF \(P. Specifically, suppose that we have \( m \) objects, and that \( r \) of the objects are type 1 and the remaining \( m - r \) objects are type 0. We select \( n \) objects at random from the population, so that all samples of size \( n \) are equally likely. If the sampling is with replacement, the sample size \( n \) can be any positive integer. If the sampling is without replacement, then we must have \( n \in \. As noted in the Introduction, if the sampling is with replacement, \( (X. If the sampling is without replacement, then \( Y \) has the hypergeometric distribution with parameters \( m \), \( r \), and \( n \). The hypergeometric distribution is studied in detail in the chapter on Finite Sampling Models. For reference, the probability density function of \( Y \) is given by. The following theorem makes this precise. Suppose that \( r. Then for fixed \( n \in \N. We can group these, in order, to form a product of \( n \) fractions. The first \( y \) fractions have the form. Each of these converges to \( p \) as \( m \to \infty \). The remaining \( n - y \) fractions have the form. For fixed \( y \) and \( n \), each of these converges to \( 1 - p \) as \( m \to \infty \). Note the difference between the graphs of the hypergeometric probability density function and the binomial probability density function. In particular, note the similarity when \(m\) is large and \(n\) small. For selected values of the parameters, and for both sampling modes, run the experiment 1. From a practical point of view, the convergence of the hypergeometric distribution to the binomial means that if the population size \(m\) is large compared to the sample size, then the hypergeometric distribution with parameters \( m \), \(r\) and \(n\) is well approximated by the binomial distribution with parameters \( n \) and \(p = r / m\). Generally, the approximation works well if \( m \) is large compared to \( n \) that \( \frac. This ensures that the variance of the hypergeometric distribution is close to the variance of the approximating binomial distribution. Now let's return to our usual sequence of Bernoulli trials \( \bs. Our next result shows that given \( k \) successes in the first \( n \) trials, the trials on which the successes occur is simply a random sample of size \( k \) chosen without replacement from \( \. In statistical terms, this means that relative to \( (X. Sufficiency is discussed in more detail in the chapter on Point Estimation. Next, if \( m \le n \) then the conditional distribution of \( Y. Designate trials \( \. Both variables have binomial distributions; the first with parameters \( m \) and \( p \), and the second with parameters \( n - m \) and \( p \). There are many deep and interesting connections between the Bernoulli trials process (which can be thought of as a model for random points in discrete time) and the Poisson process. These connections are explored in detail in the chapter on the Poisson process. In this section we just give the most famous and important result—the convergence of the binomial distribution to the Poisson distribution. For reference, the Poisson distribution with rate parameter \( r \in (0, \infty) \) has probability density function. In addition, the probability generating function is \( t \mapsto e^. Then the binomial distribution with parameters \(n\) and \(p. Also, using a basic theorem from calculus, \(\left(1 - n p. Run the experiment a few times and note the general behavior of the random points in time. Note also the shape and location of the probability density function and the mean\( \pm \)standard deviation bar. Now open the binomial timeline experiment and set \( n = 1. Run the experiment a few times and note the general behavior of the random points in time. Note also the shape and location of the probability density function and the mean\( \pm \)standard deviation bar. From a practical point of view, the convergence of the binomial distribution to the Poisson means that if the number of trials \(n\) is large and the probability of success \(p\) small, so that \(n p^2\) is small, then the binomial distribution with parameters \(n\) and \(p\) is well approximated by the Poisson distribution with parameter \(r = n p\). The condition that \(n p^2\) be small means that the variance of the binomial distribution, namely \(n p (1 - p) = n p - n p^2\) is approximately \(r\), the variance of the approximating Poisson distribution. The Normal Approximation. Open the binomial timeline experiment. For selected values of \(p \in (0, 1)\), start with \(n = 1\) and successively increase \(n\) by 1. For each value of \(n\), Note the shape of the probability density function of the number of successes and the proportion of successes. With \(n = 1. 00\), run the experiment 1. The characteristic bell shape that you should observe in the previous exercise is an example of the central limit theorem, because the binomial variable can be written as a sum of \(n\) independent, identically distributed random variables (the indicator variables). The standard score \( Z. From a practical point of view, this result means that, for large \(n\), the distribution of \(Y. Just how large \(n\) needs to be for the normal approximation to work well depends on the value of \(p\). The rule of thumb is that we need \(n p \ge 5\) and \(n (1 - p) \ge 5\) (the first condition is the significant one when \( p \le \frac. Finally, when using the normal approximation, we should remember to use the continuity correction, since the binomial is a discrete distribution. General Families. For a fixed number of trials \( n \), the binomial distribution is a member of two general families of distributions. First, it is a general exponential distribution. Suppose that \(Y\) has the binomial distribution with parameters \(n\) and \(p\), where \(n \in \N. The distribution of \( Y \) is a one- parameter exponential family with natural parameter \(\ln \left( \frac. Proof: This follows from the definition of the general exponential family. This function is sometimes called the logit function. The binomial distribution is also a power series distribution. Suppose again that \( Y \) has the binomial distribution with parameters \( n \) and \( p \), where \( n \in \N. The distribution of \( Y \) is a power series distribution in the parameter \( \theta = \frac. As before. for \( y \in \. This is the power series distribution in \( \theta \), with coefficients \( \binom. The proportion of successes in the first \(n\) trials is the random variable. The proportion of successes \(M. Vary \(n\) and \(p\) with the scroll bars and note the shape of the probability density function. For selected values of the parameters, run the experiment 1. 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You’ll have to decide for yourself if the upgrade cost and tradeoffs are worth it. Your motherboard doesn’t support more than 4. GB of RAM. Although it’s rare it’s not unheard of to have a motherboard that will support an early 6. GB of RAM. In this case you’ll still get some of the benefits of a 6. If you’re not buying bleeding edge parts, however, hardware has gotten so cheap lately that it might be time to retire the old motherboard and upgrade at the same time you’re upgrading your OS. You have legacy software or other software issues to deal with. Some software doesn’t make the transition to 6. Unlike previous versions of Windows, Windows 7 6. If by some chance you’re still using a really old legacy application for something you’ll need to either virtualize it or forgo an upgrade. Also, just because an application is 6. Photoshop and Firefox are common applications where people run into this problem. The core application is available in an updated 6. 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Using a scrap piece of flooring as a guide, cut the doorjamb with a jamb saw or flush- cut saw. Use a wood chisel as necessary to cleanly remove the cut- off piece of doorjamb and casing. Once the flooring can be laid under the doorjambs and casing, the transition strips can be installed. The transition strips hide the edge of the laminate flooring as well as the adjacent flooring and cover the necessary expansion gap. Most transition strips come with a track and can be configured in multiple ways. Fasten any transition strips and tracks to the subfloor, not the laminate floor, maintaining the 1/4. Miter or cope the ends as necessary to fit snugly against the adjacent trim or frame. Snap the transition strip into the track. To finish a laminate floor edge at the top of a staircase, many types of stair nosing are available. Measure and cut the stair nosing to fit. Using the stair nosing as a guide, determine the final edge of the laminate flooring. Be sure to cover the laminate floor edge and 1/4. This can be accomplished by installing new or salvaged baseboard, or by installing a quarter round, or shoe, molding against existing baseboard. Always install baseboards or moldings to the wall and not to the laminate floor, to preserve the floating effect of the floor system. The leading comprehensive guide on building a spiral staircase from our DIY experts. Check our photos, plans, and instruction information. There is no center support and nothing seems to be holding up this staircase but the will of God, or so promulgates the private owners of this building. Is the miraculous staircase in the Loretto Chapel just that, or is there a scientific explanation for why it? Michele B., Minneapolis, MNDEAR MICHELE: I. To create a staircase today like this using an assortment of power tools and modern hand tools would be a feat. The current private owners of the Loretto Chapel state on their website. It makes over two complete 3. It rests solely on its base and against the choir loft. The risers of the 3. Made of an apparently extinct wood species, it was constructed with only square wooden pegs without glue or nails. Any carpenter worth his salt knows what. Bryce Phelps made himself a beautiful oak spiral staircase and saved a ton of money by cutting up cheap IKEA oak countertops for the treads: I went with a 4' steel pipe from the local steel yard buying 18'. A 'Spiral Stair', by definition, is a staircase with a central column in which steps are set out in a spiral pattern. As the steps wind up the column in a corkscrew-like pattern. Shop Spiral Staircases, Stair railings & Kits, Vertical Cable Railing Inserts and more! DIY Staircase & Railings. The Staircase Tumble trope as used in popular culture. Stairs can be dangerous if you misstep and fall down, even worse depending on how long it is. Shop Menards for piral staircase systems that are easy to assemble and add drama to your home d PHOTO CREDIT: Tim Carter. My guess is the owners of the Chapel have only talked to a handful of architects, engineers or master craftsmen or they didn. The floor system is made up of joists and wood that covers the joists. The floor joists under your feet are beams not unlike steel I- beams in a skyscraper. In a typical floor system, these beams or floor joists run parallel with one another on 1. The joists are covered with plywood or other wood sheeting. The joists rest on a foundation wall or sometimes another beam that rests on a foundation wall. The weight of the entire system and anything on it is transferred to the foundation by the joists. Imagine if you had a narrow floor, meaning just two joists and you cover these with plywood. This would be very similar to a narrow foot bridge. You could walk across it and the platform or bridge would not collapse. Now you have a ramp. The normal staircase in your home is just like this, but instead of a ramp, the builder made flat steps or treads so you could climb it without slipping or sliding. A simple staircase has two beams, called stringers, and the treads of the staircase rest on these beams or are connected to them. The stair treads are no different than the wood that covers a flat floor. When the carpenter set your steps in place, the weight of the staircase was transferred to the floor below where the two stringers touch the floor. The only difference with the staircase at the Loretto Chapel is these beams or stringers have been twisted into a helix. If you took the staircase apart and just allowed the inner and outer stringers to stand there by themselves, they would do so like the flagpole just outdoors on the plaza, even though each stringer is made up of several pieces of wood glued and pegged together. They have a vested interest to make sure tourists come to see this masterpiece and that couples continue to get married in this magical building. If the owners just told you that the staircase was just a regular staircase that was resting on the floor of the chapel, you. I say this as a very modest carpenter who stands in awe of the man or men who worked together to build the staircase in the Loretto Chapel. If you are near Santa Fe, NM, I urge you to stop by and see what can be done with simple hand tools, knowledge of physics and math, and determination. |
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October 2017
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