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Bonus Prob. (30) Assume a is unknown and need to be estimated from B. B. Brand One method is to estimate a atsee Lecture notes in Chapter 12 5, cos 6, +B; sin 6. + 8 cm 24. + sis24.) The next estimator of als from the variance of Mo). Or. (-0.) do...cox + cos2x)dr where ---G-VR+Band G6+ Solve the estimator afe.d = e) from the above equation. Use the from Problem 4) to estimates. That is calculated and a, the true value is 23 A useful formula for the problem is Se cos2x dens+cos Zx from which you can derive fr cosidr= (1+2) sin x + 2x come b1,2,3,84 Po Efe **** * e-% [ ->] Sunday Poses for Halefet y e*
Bonus Prob. (10 pt) Assume a is unknown and need to be estimated from B1, B2, B3, and B4. One method is to estimate a at 0 = . (see Lecture notes in Chapter 8). i.e., 1 2 â = a1 = =+=(B, cos 0 + B2 sin , +Bz cos 24. + B4 sin 20.) TT TI The next estimator of a is from the variance of H(o). Or, 2 12 a *10 - P.) H(º) dº = 4*, *?*+cos x + cos2x)dx + Po- 27 TT . where x = 0 - 0, C1 = B} + BJ, and Cy B3 + B? Solve the estimator a (i.e., â = az) from the above equation. Use B1, B2, B3, B4 from Problem 4) to estimate a. That is calculate a, and az (the true a value is 2). A useful formula for the problem is S x2 cos 2x dx= (2x2-1) sin 2x + cos2x from which you can derive S x2 cos x dx= (x2 – 2) sin x + 2x cosx.
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