13. Find the length of the part of the curve
y=3/16e^(2x)+1/3e^(-2x) for 0<x<ln2
16 13. Find the length of the part of the curve y-で2" +-e-2x for 0-rS In 2. 29 64 13 16 16
16 13. Find the length of the part of the curve y-で2" +-e-2x for 0-rS In 2. 29 64 13 16 16
Find (g of)(13) when f(x) X-3 2 and g(x) = 3x + 1. A) 16 B) 20 Q 200 미
SHOW STEP BY STEP SOLUTION. THIS IS LINEAR SYSTEM
ANALYSIS.
a) Find frequency response, x (Fourier Series), where k is frequency index -Sksoo b) Find values of x when k1, 0, 1, 2 4 2 46 a) A Fourier Transform of rectangle is defined as T=11 2.4.2 sinc (2.2.f) 16-sinc(4.f) a) 16 4 b)-1.0000 0 1.0000 2.0000 -0.2773-0.17821 2.9091 -0.2773 0.17821 -0.3835 0.83981 So the Fourier series is x =-| 16-sincl 4-1-e , r + 16 . sinc! 4-1-e -16-sinc...
given x^2+kx+16=0, find all values that k gives:
a) two real solutions
b) one real solution
c) two complex solutions
7. Given 2? + kx + 16 = 0, find all values of k that give: (a) two real solutions (b) one real solution (c) two complex solu- tions
A cdf of X is given as follows. 0 8 16 1 2< (a) Find f(ar). (b) Find 50th percentile. (c) E(X) (d) V(x)
A cdf of X is given as follows. 0 8 16 1 2
Question 8 (Chapters 6-7) 12+2+2+3+2+4+4-19 marks] Let 0メS C Rn and fix E S. For a E R consider the following optimization problem: (Pa) min a r, and define the set K(S,x*) := {a E Rn : x. is a solution of (PJ) (a) Prove that K(S,'). Hint: Check 0 (b) Prove that K(S, r*) is a cone. (c) Prove that K(S,) is convex d) Let S C S2 and fix eS. Prove that K(S2, ) cK(S, (e) Ifx. E...
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
(dispersion) DA), standard error σ(X) , asymmn etry coefficient ASA) an 2. Calculate multiplier k. Find distribution function fe), mode Mok), median Mea), expectation value M(x), variance (dispersion) D(x), standard error σ(x), asymmetry coefficient As(x) and excess Ex(x) for continuous distributions with the given probability densities a) b) x>0 x-16sxs0 x20sxs-16 x<-20 x <2 160 f(x)=1 0 r>6 40 2 Calculate probability that X E-16:6] Calculate probability that X E [1:4]
Problem 2 - Three Continuous Random Variables Suppose X,Y,Z have joint pdf given by fx,YZ(xgz) = k xyz if 0 S$ 1,0 rS 1,0 25 1 ) and fxyZ(x,y,z) = 0, otherwise. (a) Find k so that fxyz(x.yz) is a genuine probability density function. (b) Are X,Y,Z independent? (c) Find PXs 1/2, Y s 1/3, Z s1/4). (d) Find the marginal pdf fxy(x.y). (e) Find the marginal pdf fx(x).
Problem 2 - Three Continuous Random Variables Suppose X,Y,Z have joint...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...