(b) i. (2 pts.) What is the smallest real perturbation ER E RIO -55, x < 0.5 ii. (8 pts) For the ...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
Question 2. Consider a random variable X~x20 - Answer the following. i) ii) What are E(X) and Var(X)? What value is the value xão,0.1 that satisfies P(xão > xão,0.1) = 0.1? Suppose you draw random samples of n=40 individual values from a population where the relative frequency of values follows a Chi-square distribution with 20 degrees of freedom. That is Xi~xão for every random variable in the random sample (X1 , X2 ,... X40). iii) iv) Use the Central Limit...
4. Let X have pdf (a) as follows 1) 1/2) + .2 1(1/2 < x f(z) = 1.81(0 x (8 pts) What is E[Xj? Justify your answer. (12 pts) Write Matlab or pseudocode that will produce 10, 000 PRNG samples with the dis- tribution of X. Have the output recorded in the vector a (i.e., so that (1) is the first sample, (2) is the second sample, etc.) 4. Let X have pdf (a) as follows 1) 1/2) + .2...
(b) I G)(u) and G'(1) = 2+e Ft2): 3gcx1+1α)-x'(x) faf(x) , compute G(1) and G'(1). g(5a)' 2x for 37 Problem 2 For each function below, find the smallest integer n for which f)0 and find fin-(x) or explain why this is not possible. notation: The factorial function is n!n (n -1).(n-2)3.2.1 example: If (x)2+z2-1, then n 5 andf)24.3-2.1 2(41). (a) (x)95 16z +23. (b) f(x) sin(3z). Problem 3 3 is shown to The graph of the tilted ellipse z2 -...
Stella Mars Polyte Mo 404 (Probahlty and Statsti Exam (40 poiats) all st D t o The ve distl ta f de i X (2 pts)What is PIX1/2 7 a p) Wht P/2 a/2 iSpts) Whiat is the prohability deasity function of the1audn variable whoe cdf is Fi) T LXbe it zandom vairiable with proability density ftion ot w t What is the valui of C 2tsl What is fhe rumalatjve distnibution of X oI Let X he a toitinnous...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...