The area ofthe surface described by z = /(x, y) for (x, y) in R is given by IJ\/\fAx, y)]2 + I/V(X, y)]2 + 1 dA. R Use Algorithm 4.4 with n = m = 8 to find an approximation to the area of the surface on the hemispherex 2 +y 2 + z 2 = 9, z > 0 that lies above the region in the plane described by R = {(x, y) | 0 < x < 1,0 < y < 1)

11/2/15 1.) Random values take their values from an interval of real numbers, possibly all real numbers 2.) Have a probability density function (pdf) 3.) Positive probabilities (correspond to) areas under a probability density function 4.) The entire area under a pdf is 1 x is uniform of [0,10]. More general example Uniform on [a,b] Atriangle distribution on [0,1] We need: 1.) Normal distributions 2.) “Student-t” (or just “t”) 3.) “Chi-square” (x^2) • on [0, inﬁnity] 1.) Normal Distributions: completely determined by a mean and a standard deviation. Ex.) x= height of adult human male Mean = 69 in St. Dev = 3 in y = weight of adult human male Mean = 170 St. Dev = 30 *The standard normally distributed random variable is called z and h