American history Essay Example | Topics and Well Written Essays - 1500 words - 3

American history - Essay Example The Progressive Era witnessed the appearance of reformers known by the name progressives whose objective was to knock down the devils of inequalities in the nation (Roosevelt). With the target of highlighting democratic principles and social justice, the progressives made efforts to lay the pillar for a â€Å"new† America with liberty, equality and power (Roosevelt). These progressives emerging from a tradition of middle-class elites possessed a great sense of social responsibility for the underprivileged class (Roosevelt). In the view of Eleanor Roosevelt who belonged to this social class, â€Å"In that society you were kind to the poor, you did not neglect your philanthropic duties, you assisted the hospitals and did something for the needy.† (Roosevelt). The demand put forward by the progressives started gaining recognition from farmers to politicians as it went on expanding from social service to journalism (Roosevelt). Such was the outcome of the endeavors that even president, Theodore Roosevelt mentioned: â€Å"No hard-and-fast rule can be laid down as to the way in which such work [reform] must be done; but most certainly every man, whatever his position, should strive to do it in some way and to some degree.† (Roosevelt). This was supported with Roosevelt’s resolution to discourage the laissez-faire approach and to hold up labor of 1902’s Anthracite Coal Strike settlement (Roosevelt). In the Progressive Era, ladies such as Jane Addams and Lillian Wald shouldered the social duties of updating the immigrant sections and steering them towards the right ways of life and moral values (Roosevelt). This had some influence on the woman and child labor laws, welfare benefits and factory inspection legislation (Roosevelt). However, the exertions of these female reformers simply added to the bosses’ recognition (Roosevelt). Another group of progressives were â€Å"muckraking† journalists like Jacob Riis, whose work How

Buffron Needle Problem Essay Example | Topics and Well Written Essays - 1500 words

Buffron Needle Problem - Essay Example The assumption would be that the lines are parallel to the x-axis. Two variables exist in this scenario; the angle with which the needle would be tilted to the lines, ÆŸ, and the distance between the closest line and the center, which would never exceed half the distance between the equidistant lines (See fig. 2 below) The assumption is that the needle would land at a random point between the lines and the angle of inclination would be another random variable. It should further be assumed that the random variables are a result of uniform distribution. This picture depicts the needle missing the line and the needle could only be on the line if the distance closest to a line, D would be less than or equal to  ½SinÆŸ, that is D ≠¤  ½SinÆŸ. This could be illustrated better using figure 3 below. From this, the values representing a hit would occur below or on the curve, D ≠¤ 1/2SinÆŸ. The probability of hitting the line would be computed as a ratio of the shaded curve to the area of the entire rectangle. The area under the curve would be computed using integrals between zero and Ï€. This will give a result of 1. The rectangle would have an area of  ½Ãâ‚¬. The probability of hitting the line would therefore be 1/ ( ½Ãâ‚¬) = 2/Ï€, which is approximately 0.6366. To work out Ï€, the number of needle drops, say N would be multiplied by two and then divided by the number of hits, N’. That is: This would be a situation where the needle is long and its length, l, would be greater than the distance between the equidistant lines. Hence, x = l/d > l. The probability that the needle would intersect a line would be computed using the expression below: Consider the size parameter x = l/d. Taking N as the number of crossings and n as the tosses made by a short needle of size parameter x, then N would have a binomial distribution as a function of n and 2x/Ï€. The point estimator with regard to