3. The following four facts are given about a real signal xn with Fourier trans- form...
We are given the following information about a signal x(t) a) t) is real and odd. b)x(t) is periodic with period T 2 and has Fourier coefficients a a,-0 for Ikl > 1. d) 2 Identify two possible signals that satisfy these properties.
{x_n} and {y_n} are sequences of positive real numbers AC fn→oo > O, prove tha m in yn lim xn 0 implies lim yn_0
n. 7. Let Xi, , Xn be iid ;0) =-e-r2/0 where x > 0. Sho w that θ=「x? is based on f (x efficient.
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To implement Fourier Series (t)---> (ults) -1 1 0 t---> (sec) (ii) To= Wo=- Do- Dn= Sketch D vs nw.. (vi) Sketch <D, (e.) vs nw.. (vii) Power of r(t) = (viii) Express x(t) as sum of Sine Waves, Cosine waves and DC (ix) Show that the expression found in part(viii) is real
Let X1, X2,.. .Xn be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of θ, θ. Use this maximum likelihood estimator to obtain an estimate of P[X > 4 when 0.50, 2 1.50, x 4.00, 4 3.00.
2. Suppose X1, X2, . .., Xn are a random sample from θ>0 0, otherwise Note: If X~fx(a; 0), thenXEx(0). (a) Find the CRLB of any unbiased estimator of θ (b) Is the MLE for θ the MVUE?
Please prove this, thanks! 2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.
only number 8 Figure 3.2 Figure 3.1 Find the Fourier transform of the following signals a. x(t) - e-at cos(wt) u(t) ,a>0 8. 1+j2)t 9. Compute the discrete Fourier transform of the following signals.
1. Let Xn = 2 - 3 a) To what value x does xn converge? b) Find the smallest n, such that n > n. = |xn – x] < 0.1. c) Find the smallest no such that n > no [xn – x] < 0.005. d) Find the smallest no such that n > no = |xn – x] < 10-6. e) Find the smallest no such that n >no = |xn – x] < E.
1. [8 points] Suppose Xi... Xn is a random sample from a Pareto distribution with the density If x > 1 otherwise, where ? > 1, Find the method of moments estimator of ?.