## Introduction to mathematical statistics |

### From inside the book

Results 1-3 of 49

Page 219

For each x e {jc; 0 < x < 00 }, there exists at least one positive member of the

family of

=0 for every 8 > 0 requires u(x) =0 at every point x at which at least one member

of ...

For each x e {jc; 0 < x < 00 }, there exists at least one positive member of the

family of

**probability density functions**. So we could say we shall show that ElufX)-]=0 for every 8 > 0 requires u(x) =0 at every point x at which at least one member

of ...

Page 220

Let u(x) denote a continuous function of x (but not a function of 8). If E[u(X)] = 0 for

every 8, 8 e Q, requires u(x) to be zero at each point x at which at least one

member of the family of

...

Let u(x) denote a continuous function of x (but not a function of 8). If E[u(X)] = 0 for

every 8, 8 e Q, requires u(x) to be zero at each point x at which at least one

member of the family of

**probability density functions**is positive, then the family of...

Page 222

If the family {g^y^, 8); 8e Q} is complete, the continuous

at each point y1 at which at least one member of the family is positive. That is, at

all points of nonzero

...

If the family {g^y^, 8); 8e Q} is complete, the continuous

**function**<p(yi) ~ tiVi) = 0at each point y1 at which at least one member of the family is positive. That is, at

all points of nonzero

**probability density**, we have, for every continuous unbiased...

### 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 Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere