Thgonr soio of th ysium and stalth a point. (c) X 2-1 2 1 2 0X (n) (d) Xn1) -1 0 2
c. 2 d. 3 3 5. Find the absolute maximum of the function Ax)-xx+ 1)0x-1) on the interval 0sx2. b. 0 d. 8 Find the slope of the tangent to the graph of -x(x2-*) at its point of infection. 6. a. 0 b. 2 c. 4
2 Consider x2 if x <0 f (x) = 2x+ 1 if 0x < 2 (a) Determine whether f is continuous on the interval [0, 1]. (b) Determine whether f is right continuous on the interval [0, 1]. (c) Determine whether f is continuous on the interval [1,2].
8. Let 02 (1)e, 00; x > 0 -0x f(x) = 1 +0 (a) Show that f(x) is a probability density function (b) Find P(X > x) (c) Find the failure rate function of X
(d) Show that the point ro 0 is a regular singular point for the equation and that the solution about the point 20 0 can be written as where x>0 (2n-1)]], [n!1.3.5 , Lnsl
(d) Show that the point ro 0 is a regular singular point for the equation and that the solution about the point 20 0 can be written as where x>0 (2n-1)]], [n!1.3.5 , Lnsl
1. Consider the density f (x) = 0x-1 for 0 < x <1 and 0 otherwise You have data 0.4, 0.6, and 0.8 that is a random sample from this density a. Find the method of moments estimate for 0 b.Find the MLE for 0
> + x 0. x)e-0, f(x) = fall + x)e-0x tu function. That is, shou is, show that > where (a) Show that f(x) is a density fun What is f(x) > 0, and that bo f(x) dr = 1. (b) Find ELI (c) Find Var(37)
th fu + + + + X + + 1-2 f(x) = {0 2 if x < 0 if x = 0 if x > 0 50. the graph of y = f(x) is shown above, which of the following statements must be true? I. f(x) > 0 II. f(x) = -f(-x) III. If x < x2, then f(x) = f(x2) (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II,...
6-x-4, 0x<2 0 1 2cych Exri If for two R.V. s X&Y the joint pdf is given by, otherwise Find Frix (o (1), Frix (alt), Ely/x-1]. var [Ylx-i] = E[^\x-]- (E[1\x=1])!
-xoe x Bar (6) x >0x>0, B > 0 Homework If x ~ Gamma (2,3) Find E(X ) - E (x4) - Elx"), K is a positive © E (x ) integar Xmf(x) dx can M, Variance: 82 2012 Ean : M Standard deviation - o 1 - 2
0 c 10 c N,D 15 c Fig. 1 (2 point) Please derive L and Lm of the FSM in Fig. 1 if the state 15c is a final state.
0 c 10 c N,D 15 c Fig. 1
(2 point) Please derive L and Lm of the FSM in Fig. 1 if the state 15c is a final state.