Free Essays on Beouwulf

Title Beowulf, an epic poem, was written around the ninth century A.D., and was also written in Old English. Beowulf was authorized by a Roman Catholic Priest, which is acknowledged due to numerous references to the Bible. Beowulf, the main character is a mighty warrior with great pride and concern for his fellow comrades and The Land of the Geats. Throughout the poem there are several challenges that Beowulf has to confront. The first is the battle with Grendel, a horrific monster, because he has been terrorizing the Geats. Beowulf defeats Grendel in the battle but has to face another one with Grendel’s mother who wants to get revenge for the death of her son. Beowulf finally defeats Grendel’s mother. In the third battle Beowulf has to fight a dragon that has wreaked havoc on the Geats society due to a servant that had stolen a golden goblet from his home. The dragon was defeated with the help of a young kinsman, Wiglaf, but not before biting Beowulf in the neck and eventua lly destroying him. Although dying, Beowulf was glad that he had won the treasure for his people. The second poem is Sir Gawain and the Green Knight, which is a romance written about six hundred years ago. The author is known as the Pearl Poet. This poem is a moral allegory, which means that the poem is glorified in a way, but also represents a moral idea. This poem is about a knight that has to go and find the Green Chapel where a Green Knight lives and respectfully get his head cut off just like he did to him. This called the ‘Beheading Game†. Both of these poems characters illustrate right living, the consequences of failing to live rightly, and the rewards of it. In the poem â€Å"Beowulf†, Beowulf illustrates various ways of how to live rightly. The first is when he went out by himself to conquer Grendel and Grendel’s mother. Beowulf went out to fight Grendel and his mother because he knew that he had to do a favor for Hrothgar. When Beowulf was yo... Free Essays on Beouwulf Free Essays on Beouwulf Title Beowulf, an epic poem, was written around the ninth century A.D., and was also written in Old English. Beowulf was authorized by a Roman Catholic Priest, which is acknowledged due to numerous references to the Bible. Beowulf, the main character is a mighty warrior with great pride and concern for his fellow comrades and The Land of the Geats. Throughout the poem there are several challenges that Beowulf has to confront. The first is the battle with Grendel, a horrific monster, because he has been terrorizing the Geats. Beowulf defeats Grendel in the battle but has to face another one with Grendel’s mother who wants to get revenge for the death of her son. Beowulf finally defeats Grendel’s mother. In the third battle Beowulf has to fight a dragon that has wreaked havoc on the Geats society due to a servant that had stolen a golden goblet from his home. The dragon was defeated with the help of a young kinsman, Wiglaf, but not before biting Beowulf in the neck and eventua lly destroying him. Although dying, Beowulf was glad that he had won the treasure for his people. The second poem is Sir Gawain and the Green Knight, which is a romance written about six hundred years ago. The author is known as the Pearl Poet. This poem is a moral allegory, which means that the poem is glorified in a way, but also represents a moral idea. This poem is about a knight that has to go and find the Green Chapel where a Green Knight lives and respectfully get his head cut off just like he did to him. This called the ‘Beheading Game†. Both of these poems characters illustrate right living, the consequences of failing to live rightly, and the rewards of it. In the poem â€Å"Beowulf†, Beowulf illustrates various ways of how to live rightly. The first is when he went out by himself to conquer Grendel and Grendel’s mother. Beowulf went out to fight Grendel and his mother because he knew that he had to do a favor for Hrothgar. When Beowulf was yo...

What Is the Cauchy Distribution

What Is the Cauchy Distribution One distribution of a random variable is important not for its applications, but for what it tells us about our definitions. The Cauchy distribution is one such example, sometimes referred to as a pathological example. The reason for this is that although this distribution is well defined and has a connection to a physical phenomenon, the distribution does not have a mean or a variance. Indeed, this random variable does not possess a moment generating function. Definition of the Cauchy Distribution We define the Cauchy distribution by considering a spinner, such as the type in a board game. The center of this spinner will be anchored on the y axis at the point (0, 1). After spinning the spinner, we will extend the line segment of the spinner until it crosses the x axis. This will be defined as our random variable X. We let w denote the smaller of the two angles that the spinner makes with the y axis. We assume that this spinner is equally likely to form any angle as another, and so W has a uniform distribution that ranges from -Ï€/2 to Ï€/2. Basic trigonometry provides us with a connection between our two random variables: X tanW. The cumulative distribution function of X is derived as follows: H(x) P(X x) P(tan W x) P(W arctanX) We then use the fact that W is uniform, and this gives us: H(x) 0.5 (arctan x)/Ï€ To obtain the probability density function we differentiate the cumulative density function. The result is h(x) 1/[Ï€ (1 x2) ] Features of the Cauchy Distribution What makes the Cauchy distribution interesting is that although we have defined it using the physical system of a random spinner, a random variable with a Cauchy distribution does not have a mean, variance or moment generating function. All of the moments about the origin that are used to define these parameters do not exist. We begin by considering the mean. The mean is defined as the expected value of our random variable and so E[X] ∠«-∞∞x /[Ï€ (1 x2) ] dx. We integrate by using substitution. If we set u 1 x2 then we see that du 2x dx. After making the substitution, the resulting improper integral does not converge. This means that the expected value does not exist, and that the mean is undefined. Similarly the variance and moment generating function are undefined. Naming of the Cauchy Distribution The Cauchy distribution is named for the French mathematician Augustin-Louis Cauchy (1789 – 1857). Despite this distribution being named for Cauchy, information regarding the distribution was first published by Poisson.