Mathematics, 22.04.2020 01:47 minasotpen1253
Here is a probabilistic method for computing the area of a given subset S of the unit square. The method uses a sequence of independent random selections of points in the unit square [0,1]•[0,1], according to a uniform probability law. If the ith point belongs to the subset S the value of a random variable Xi is set to 1, and otherwise it is set to 0. Let X1,X2,... be the sequence of random variables this defined, and for any n, let Sn=(X1+X2+...+Xn)/n. a)Show that E[Sn] is equal to the area of the subset S, and that var(Sn) diminishes to 0 as n increases. b)Show that to calculate Sn, it is sufficient to know Sn-1 and Xn, so the past values of Xk, k=1,...,n-1, do not to be remembered. Give a formula. c) Write a program to generate Sn for n=1,2,...,10000, using the computer’s random number generator, for the case where the subset S is the circle inscribed within the unit square. How can you use your program to measure experimentally the value of pi. d) Use a similar computer program to calculate approximately the area of the set of all (x, y) that lie within the unit square and satisfy 0<=cos(pi•x) + sin(pi•y) <= 1
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Aswimming pool had 2.5 million liters of water in it. some water evaporated, and then the pool only had 22 million liters of water in it. what percent of the water evaporated?
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Mathematics, 22.06.2019 00:30
Use the irregular polygon below. show all work. a. find the perimeter. b. find the area. the angles of the irregular polygon is 2, 8, 8, and 4.
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Here is a probabilistic method for computing the area of a given subset S of the unit square. The me...
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