Let exp(-т*) + vk Yk where dent M and V N(0, o2 are mutually indepen R, k = 1, (a) Construct the likelihood T(y|x) and...
Let d ln(B)e where the unknown 3 E R, k = 1,..., M and ek are dent and identically distributed according to the (standard) Cauchy distribution, that is mutually indepen- 1 1 т (еx) k (a) Construct the likelihood T(d|B) and the negative log-likelihood (b) In this case, you cannot find an likelihood estimate BML But do this: derive the nonlinear equa- explicit form for the maximum tion of the form (- In т(d|B)) — F(83; d,, .., dм) dp...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...