## Introduction to Mathematical Statistics |

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Page 73

Thus, solving for 21 and 22 in terms of vi and yo, we have z = wisy) and 22 =

wasya) so that w'i(yi) 0 J = = w'i(yi)w',(yi) # 0. 0 w'2(y2) Hence the joint

and Y, is g(yi, y) = fi[wi(yi)]f.[w:{y.)]|w'i(yi)w',(yi), (y1, y2)e:B, = 0 elsewhere ...

Thus, solving for 21 and 22 in terms of vi and yo, we have z = wisy) and 22 =

wasya) so that w'i(yi) 0 J = = w'i(yi)w',(yi) # 0. 0 w'2(y2) Hence the joint

**p.d.f. of Yi**and Y, is g(yi, y) = fi[wi(yi)]f.[w:{y.)]|w'i(yi)w',(yi), (y1, y2)e:B, = 0 elsewhere ...

Page 81

This is the result that has an important role in subsequent chapters. Here we took

X1, X2, ..., Xn to be a random sample from a continuous type of distribution and

showed that

This is the result that has an important role in subsequent chapters. Here we took

X1, X2, ..., Xn to be a random sample from a continuous type of distribution and

showed that

**Yi**= K(X) + K(X2) + ... + K(X.) has a**p.d.f.**having the form (2).Page 100

Since we are dealing with random variables of the discrete type, no Jacobian is

involved, and at points of nonzero probability the joint p.d.f. of Y, and Y, is 49*(1 -

0)-v. (y – yo)!ya!(2 – y + y2)!(2 – yo)! If this joint

Since we are dealing with random variables of the discrete type, no Jacobian is

involved, and at points of nonzero probability the joint p.d.f. of Y, and Y, is 49*(1 -

0)-v. (y – yo)!ya!(2 – y + y2)!(2 – yo)! If this joint

**p.d.f. of Yi**and Y, is divided by ...### What people are saying - Write a review

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere