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

Buffron Needle Problem - Essay ExampleThe assumption would be that the tunes are parallel to the x-axis. cardinal 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 haphazard 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 Sin, that is D Sin. This could be illustrated pause using figure 3 below.From this, the values representing a hit would occur below or on the curve, D 1/2Sin. The probability of hitting the line would be computed as a ratio of the sh aded curve to the area of the entire rectangle. The area under the curve would be computed using integrals between zero and . This willing 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 turn up , the number of needle drops, say N would be multiplied by two and then divided by the number of hits, N. That isThis 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 belowConsider 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/. The point estimator with regard to