Approximate solution

1.7.19. Employ 2 digit arithmetic with rounding to oompute an approximate solution of the linear system 0.23: + 2y 32: = 6, 5:1: + 433; + 272 = 58, 3m + 233; 42;: = 87, using the following methods: (a) Regular Gaussian Elimination with Back Substitution; (1)) Gaussian Elimination with Partial Pivoting; (6) Gaussian Elimination with Full Pivoting. ((1) Compare your answers and discuss their accuracy. Consider the bivariate joint PDF of X and Y given by (c is some constant) fxy (u, v) = otherwise 1. Find the value of c. 2. Find p(X Sys 3. Find fy(v) the marginal distribution of Y. 4. Compute p(Y |Y = ) 9. Determine whether X and Y are independent.Let X1 , . .. . Xn N (H, 62), let Fn (1) = = n 1=1 denote their empirical distribution, and let @,2 denote the cdf of the distribution N (1, 62). Recall that in the Kolmogorov-Smirnov test, we considered the test statistic T, = Vn sup |F, (1) - @,.621 ER In the Kolmogorov-Lilliefors test, we consider the test statistic Tn = Vnsup |F, (1) - Qua IER It is true or false that T, and T' , have the same distribution for for all n E N? (Refer to the slides.) O True False