## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 12

Page 96

In accordance with the theorem of Section 3.3, page 56, the statistic X = (X, + X, +

... + X)/9 is normal with mean 6 and variance or” = 1/9. Thus X is an

In accordance with the theorem of Section 3.3, page 56, the statistic X = (X, + X, +

... + X)/9 is normal with mean 6 and variance or” = 1/9. Thus X is an

**unbiased****statistic**for 6. The statistic X1 is also normal with mean 6 and variance ax,” = 1; ...Page 104

Show that the nth order statistic of a random sample of size n from the uniform

distribution having p.d. f. f(x; 6) = 1/0, 0 < r ... Let Y. = u2(X1, X2,..., X.) be another

statistic (but not a function of Y, alone) which is an

...

Show that the nth order statistic of a random sample of size n from the uniform

distribution having p.d. f. f(x; 6) = 1/0, 0 < r ... Let Y. = u2(X1, X2,..., X.) be another

statistic (but not a function of Y, alone) which is an

**unbiased statistic**for 6; that is,...

Page 106

Let Y = u(X1, X2, ..., Xn) be a sufficient statistic for 0, and let Y = u2(X1, X2,..., X.),

not a function of Yi alone, be an

defines a statistic q(Yi). This statistic q(Y) is a function of the sufficient statistic for

6; ...

Let Y = u(X1, X2, ..., Xn) be a sufficient statistic for 0, and let Y = u2(X1, X2,..., X.),

not a function of Yi alone, be an

**unbiased statistic**for 6. Then E(Yaly) = b(yi)defines a statistic q(Yi). This statistic q(Y) is a function of the sufficient statistic for

6; ...

### 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