Question

1. Suppose X has p.d.f. f(x) = .513r?e^^*, x > 0. Using the data below, find the maximum likelihood estimate for A 6.73 3.63 6.11 2.55 4.12 6.71 6.27 8.51 7.91 5.14 8.46 6.08 7.97 4.49 3.34 2.344.17 6.57 5.05 5.22 2. Using the estimate you found in Problem 1, give the maximum likeihood estimate for and 2

Answer 1

11 Ms I Given that f(x) = 0.57 x 2 x The likelihood tunction is L(x, t) - f(x;) =(1529" ? log2 (2, 1) = alogo.5 + 3 n log x + ² log x? 1 x;

Ditterentiating with respect to 1 Blog 2 0 => -&x=0 in AH in maximum likelihood estimator (MLE) of f is û = 3n 2002X; in the estimate is a co UUMUS f = 3x20 - 0.5387 VI.37 2. From (1) î = 0.5387 Let g, (x) = 3 it is a one one to one tunition 9,62 - 3 / 3 .: ML estimate of - 3 = 5.569 0.5387

het 9 (X) = 3 4 5 For 270 9₂ is one one to one function. -9,11) :: Mi estimate of info_52875* = 103