## Introduction to Mathematical Statistics |

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Page 18

The

expectation (or expected value) of u(X) and is denoted by E[u(X)]. That is, Hol-

suese is, if X is a continuous type of random variable, or E[u(X)] = XXu(x)/(x), if X

is a ...

The

**integral**, or the sum, as the case may be, is called the mathematicalexpectation (or expected value) of u(X) and is denoted by E[u(X)]. That is, Hol-

suese is, if X is a continuous type of random variable, or E[u(X)] = XXu(x)/(x), if X

is a ...

Page 19

The n-fold

mathematical expectation, denoted by E[u(X1, X2, ..., Xn)], of the function u(X1,

X2, ..., X,). In this paragraph we shall point out some fairly obvious but useful facts

about ...

The n-fold

**integral**(or the n-fold sum, as the case may be) is called themathematical expectation, denoted by E[u(X1, X2, ..., Xn)], of the function u(X1,

X2, ..., X,). In this paragraph we shall point out some fairly obvious but useful facts

about ...

Page 36

It is proved in books on advanced calculus that the

for k > 0 and that the value of the

called the gamma function of k and we write T(k) = s go-le-way. If k = 1, clearly oo

...

It is proved in books on advanced calculus that the

**integral**s go-le-way 0 existsfor k > 0 and that the value of the

**integral**is a positive number. The**integral**iscalled the gamma function of k and we write T(k) = s go-le-way. If k = 1, clearly oo

...

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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