## Introduction to Mathematical Statistics |

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Page 14

tions which will not be enumerated here), we say that the two

and Y are of the discrete

that

tions which will not be enumerated here), we say that the two

**random**variables Xand Y are of the discrete

**type**or of the continuous**type**, and have a distribution ofthat

**type**, according as the probability set function P(A), A C A, is defined by ...Page 15

Similarly, after extending the definition of a p.d.f. of the discrete

for one

XX f(x, y), and so on. In accordance with this convention (of extending the ...

Similarly, after extending the definition of a p.d.f. of the discrete

**type**, we replace,for one

**random**variable, Xi(x) by X's.), and, for two**random**variables, XXI(x, y) byXX f(x, y), and so on. In accordance with this convention (of extending the ...

Page 18

Let X be a random variable having a p.d.f. f(z), and let u(X) be a function of X

such that s u(z)f(z) dz exists, if X is a continuous

that Xu(x)/(x) exists, if X is a discrete

...

Let X be a random variable having a p.d.f. f(z), and let u(X) be a function of X

such that s u(z)f(z) dz exists, if X is a continuous

**type of random**variable, or suchthat Xu(x)/(x) exists, if X is a discrete

**type of random**variable. The integral, or the...

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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