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

Buffron Needle Problem - Essay suitThe assumption would be that the drags argon parallel to the x-axis. Two variables exist in this scenario the angle with which the needle would be tilted to the lines, , and the distance betwixt 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 peer to Sin, that is D Sin. This could be illustrated better using figure 3 below.From this, the values representing a hit would occur below or on the turn, D 1/2Sin. The probability of hitting the line would be computed as a ratio of the shaded curve to the ambit of the entire rectangle. The area under the curve would be computed using integrals between zero and . This will give a result of 1. The rectangle would have an area of . The probability of hitting the line would therefore be 1/ () = 2/, which is approximately 0.6366. To work unwrap , the number of needle drops, say N would be multiplied by two and then shared out by the number of hits, N. That isThis would be a situation where the needle is long and its length, l, would be great 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 belowConsider the size parameter x = l/d. Taking N as the number of crossings and n as the tosses made by a rook needle of size parameter x, then N would have a binomial distribution as a function of n and 2x/. The point estimator with regard to