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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Mathematics, 22.06.2019 02:30
Otto used 6 cups of whole wheat flour and cause x cups of white flour in the recipe. what is the equation that can be used to find the value of y, the total amount of flour that otto used in his recipe and what are the constraints on the value of x and y? a y=6x; x is any interger greater than the equal to 0 and y is an interger greater than the equal to 6? b y=6x; is any real number greater than or equal to 0 and y is any real number greater than or equal to 6? c y=+6; x is any intger greater than or equal to 0 and y is an intger greater than or equal to 6? d y=x+6; x is any real number greater than 0 eqaul to 0 and y is any real number greater than or eqaul to 6? [someone answer this with a b c or d simplyactaully answer it this took forever to type on my phone] you. ill even raise the number of points get
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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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