## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 18

Page 143

variable Y depends upon the positive integer n, in this chapter we shall write the

moment-generating function of Y in the form

which is essentially Curtiss' modification of a theorem of Lévy and Cramér,

explains ...

variable Y depends upon the positive integer n, in this chapter we shall write the

moment-generating function of Y in the form

**My**(**t**; n). The following theorem,which is essentially Curtiss' modification of a theorem of Lévy and Cramér,

explains ...

Page 147

If a "t”/2 is added and subtracted, then _ go sm."(3) - 0°lso m(t) = 1 + 2 + 2 as was

to be shown. Next consider

o - E. : :"...o - EloHo- e - e. H.W. *-*] – łęso *-*]!" -[x(...)]. - “... < *. mo - 1 +of+log+* ...

If a "t”/2 is added and subtracted, then _ go sm."(3) - 0°lso m(t) = 1 + 2 + 2 as was

to be shown. Next consider

**My**(**t**; m) where l to: t -**My**(**t**; n) = ELe "V" t(Xi-A) toxa-u)o - E. : :"...o - EloHo- e - e. H.W. *-*] – łęso *-*]!" -[x(...)]. - “... < *. mo - 1 +of+log+* ...

Page 225

Now #2 My() = My(0) + M, (0) + Mov(0); +... = 1 +te(V) +;E(Y) + ..., so that E(V*) is

the coefficient of to/k! in the expansion of

, so all derivatives of

Now #2 My() = My(0) + M, (0) + Mov(0); +... = 1 +te(V) +;E(Y) + ..., so that E(V*) is

the coefficient of to/k! in the expansion of

**My**(**t**) in powers of t. Here**My**(**t**) =**My**(—**t**), so all derivatives of

**My**(**t**) of odd order vanish when t = 0. Accordingly E(V) ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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