6. Show that for a > 1/2, lim s W(1/s) s-+0 where the Iimit is taken in the mean square senuse.
Please answer the question and WRITE LEGIBLY - thanks 6. Show that for a > 1/2, s-0 where the limit is taken in the mean square sense. 6. Show that for a > 1/2, s-0 where the limit is taken in the mean square sense.
Question 2. (20 points) Suppose that a, >0 a) Show that if lim (ja the series Σ-a, diverges. a) Show that if for some r, rl>1 lim (r'a,)-< 00 then the series Σ001aj converges en the sertes Question 2. (20 points) Suppose that a, >0 a) Show that if lim (ja the series Σ-a, diverges. a) Show that if for some r, rl>1 lim (r'a,)-
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+ 40 Show the following results. 1-e2...
about the line y -1. 2. (10%) Given the graph of y = U(x) as shown, and it is known that for 0 sx <2, for 2 4 3(1-2*) for z > 4. 0 ) (ii) lim U(6) Evaluate () (U(2)+1), (l (iv) U'(4),(v) lim U() [Show succinctly your calculation or argument.] P.2 of 6 about the line y -1. 2. (10%) Given the graph of y = U(x) as shown, and it is known that for 0 sx 4....
Question 3 [10 marks Let W Then the p.d.f. 1 fw (w) 2"/21 (n/2) exp(-w/2) w3-1, w>0. and the c.d.f. is denoted as Fw (w) (a) Show that 0, n > 0, and (i) The function fw(w) is a p.d.f. (i.e., that fw(w) 2 0 for w Jo fw(w)dw 1). (ii) The mode of W is n - 2 for n > 2. (b) As n oo, W becomes normally distributed with mean n and variance 2n. This has led...
Question 3 (20 Points For each spectral density function defined below, determine the mean-square value of the random process. Show your work for full credit. ω) = else (2π)2 +25 (2mf+37(2)2+36 (s+0.5)(s-0.5) ω2 +25 w" +37a, 2 +36 TO (a)- Question 3 (20 Points For each spectral density function defined below, determine the mean-square value of the random process. Show your work for full credit. ω) = else (2π)2 +25 (2mf+37(2)2+36 (s+0.5)(s-0.5) ω2 +25 w" +37a, 2 +36 TO (a)-
Exercise 3.16: A sample of n independent observations is taken on a rv. X having a logarithmic series distribution, x=1, 2, EWT-0), , x In . Show that the MLE θ of θ where θ is an unknown parameter in the range (0,1) satisfies the equation e+ ž(1-0) ln(1-9-0, Fuercio ti tample mean. Find the asymptotie distribution oftå. Exercise 3.16: A sample of n independent observations is taken on a rv. X having a logarithmic series distribution, x=1, 2, EWT-0),...
3 square root w+1=6
please help !!!! 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
please show all steps Consider the "doomsday" model: al = - rp (1 - 2 where r, K > 0. For what values of P(0) do we have that lim P(t) = 0, where T is a finite time called the "doomsday".
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