public class RightTriangle ( public int hypotenuse () [ private int base: return this -hypotenuse; private int height; private int hypotenuse; public void metBase (int newBans) public RightTriangle thin baco - nowBang [int bane; int height) get Hypotenuse ( ) this baoo - babe; this, height . height, getHypotempo () : public void setlleight (int newileig this. height . nowHeight ; set Hypotenuse ( ) public int base () { return chin , baser private void notHypotenuse () this. hypotenuse = (int) Math rou public int height ( Math. Dact (bage *base + height whoi return this . haight, and RightTriangle.8. An important distribution in the multivariate setting is the multivariate normal distribution. Let X be a random vector in RK. That is X1 X2 X = X ... with X1, X2, ..., Xx random variables. If X has a multivariate normal distribution, then its joint pdf is given by 1 (x) = (27)k/2 ( det 2) 1/2 exp -2(x -1) 72-1(x-1) with parameters #, a vector in R", and E, a matrix in R*x*. > is the covariant matrix. Note that det > is the determinant of matrix E. And E(X1 ) E(X 2) H = E(Xk) (a) Consider the bivariate case where k = 2. Let of and o2 be the standard deviations of r.v. X1 and X2 respectively. Let p be their correlation coefficient. Determine the form of E, the covariate matrix, in terms of 61, 02 and p12. (b) If X] ~ N(0, 3), X2 ~ N(0, 4), p = -1/4 and it is known that X = [X1 X2]" has a bivariate normal distribution. Determine the joint pdf of (X1, X2).Problem 1 [4 + 4 = 8 points]. 1) Given the following four Markov chains with 2, 3, 4, 5 states respective recurrent class in each Markov chain is periodic or not. (a) (b) (c) 2) Now assume that you are given a N-state Markov chain, in which each st connections with its two neighboring states (i.e., the neighboring states of S neighboring states of S are S, and 53. ...and the neighboring states of Sy Identify under what conditions (i.e., what values of ) will this N-state periodic recurrent class, and justify your answer. Download Attachments ap Image jog Pimedia.5e2 png media 194.10 ping If photNoGux ong Skip queation . Comments Flag question Subject, Statistics and Procability e