## Introduction to Mathematical Statistics |

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Page 10

when A is two-dimensional (and

and Y); or P(A) - Pr[(Xi, X2, ..., X.)e A], when A is n-dimensional (and

there are m random variables X1, X2, ..., Xn). Each of the symbols XeA, (X, Y)éA,

...

when A is two-dimensional (and

**accordingly**there are two random variables Xand Y); or P(A) - Pr[(Xi, X2, ..., X.)e A], when A is n-dimensional (and

**accordingly**there are m random variables X1, X2, ..., Xn). Each of the symbols XeA, (X, Y)éA,

...

Page 77

ri and r2 degrees of freedom, respectively, then F = ; has the immediately

preceding p.d.f. gi(f). The distribution of this random variable is usually called an

F ...

**Accordingly**, if U and V are stochastically independent chi-square variables withri and r2 degrees of freedom, respectively, then F = ; has the immediately

preceding p.d.f. gi(f). The distribution of this random variable is usually called an

F ...

Page 172

If there is another critical region of size o, denote it by A.

uses the critical region C and the test that uses the critical region A have the

same power a when 6 = 6'. That is, ow = J; Juoz, • '', wn) dai ... daon = J.; slo, 21, •,

•' ...

If there is another critical region of size o, denote it by A.

**Accordingly**the test thatuses the critical region C and the test that uses the critical region A have the

same power a when 6 = 6'. That is, ow = J; Juoz, • '', wn) dai ... daon = J.; slo, 21, •,

•' ...

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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