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let x1 xnnbspbe iid binary random variables with pxinbsp 1 p using the pdf of the beta distribution ba b as the prior
let x1 xnnbspbe iid from a continuous cdf f on r and x0 be a future observation that is independent of xis and has the
let xi i 1 2 be independent with the pdfs lambdaie-lambdaixi0infinx i 1 2 respectivelya let theta lambda1lambda2
let x1 xnnbspbe iid from ntheta theta with an unknown theta gt 0 find a pivotal quantity and use it to construct a
for the system in sec 81 the eigenvector for the first mode was determined by the gauss elimination method complete the
in the method of cofactors app c4 the cofactors of the horizontal row and not of the column must be used explain
draw a few other diagrams of systems equivalent to fig p86 and determine the eigenvalues and eigenvectors for and m
let xi1 xininbsp i 1 2 be independently distributed as the beta distributions with pdfs thetaixthetai-1i01x i 1 2
let xi i 1 2 be independent observations from the gamma distributions gammaa gamma1 and gammaa gamma2 respectively
let x1 xnnbspbe iid from the discrete uniform distribution on 1 theta where theta is an integer ge 2 find a level
let xi1 xininbsp i 1 2 be two independent samples iid from the uniform distributions u0 thetai i 1 2 respectively
let x1 y1 xn yn be iid random 2-vectors having the bivariate normal distribution with ex1nbsp ey1nbsp 0 varx1 sigma2x
in the previous exercise derive approximations to the umpu tests by considering the limiting distributions of the test
let x x isin rn all components of x are nonzero and g be the group of transformations gx cx1 cxn c gt 0 show that a
let x1 xnnbspbe iid from nmicro sigma2 with unknown micro and sigma2 consider the problem of testing h0 micro 0
let x1nbspand x2nbspbe independently distributed as the exponential distributions e0 thetai i 1 2 respectively define
determine the equations of motion for the system shown in fig p726 solve the equations numerically in matiabo for
let h0nbspand h1nbspbe simple and let alpha isin 0 1 suppose that tlowastnbspis a ump test of size alpha for testing
let f1nbspand f2nbspbe two cdfs on r show that f1x le f2x for all x if and only if int gxdf2x le intgxdf1x for any
the following families have monotone likelihood ratioa the double exponential distribution family detheta c with a
show that if there is a location invariant estimator t0nbspof micro with finite mean then e0t xd d is finite as p for
let x1 xnnbspbe iid from the double exponential distribution demicro 1 with an unknown micro isin r under the squared
let t be a location invariant estimator of micro in a one-parameter location problem show that t is an mrie under the