## Introduction to Mathematical Statistics |

### From inside the book

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Page 9

Had we elected to

note that 4 P(A) = ... If A is one-dimensional, one random variable X is

this space; if A is two-dimensional, two random variables X and Y are

...

Had we elected to

**define**the set function P(A) in an equally arbitrary way by Wenote that 4 P(A) = ... If A is one-dimensional, one random variable X is

**defined**onthis space; if A is two-dimensional, two random variables X and Y are

**defined**on...

Page 94

These considerations actually motivate the

of X1 and X2, page 42. We now proceed to generalize the definitions of a

conditional p.d.f. and a conditional expectation. Let f(x1, x2, ..., z) be the joint p.d.f.

of ...

These considerations actually motivate the

**definition**of stochastic independenceof X1 and X2, page 42. We now proceed to generalize the definitions of a

conditional p.d.f. and a conditional expectation. Let f(x1, x2, ..., z) be the joint p.d.f.

of ...

Page 114

If fiz(x1, x2) > 0, the function f(za, ..., zn|z1, z2) is

2.) n > 2, f(za, ..., zn|z1, z) = fiz(x1, x2) ' and f(xs, ..., zn|z1, z2) is called the

conditional p.d.f. of Xa, ..., Xn, given X1 = 2, and X2 = 22. Further, the function f(z,,

...

If fiz(x1, x2) > 0, the function f(za, ..., zn|z1, z2) is

**defined**by the relation f(zi, 22, ''',2.) n > 2, f(za, ..., zn|z1, z) = fiz(x1, x2) ' and f(xs, ..., zn|z1, z2) is called the

conditional p.d.f. of Xa, ..., Xn, given X1 = 2, and X2 = 22. Further, the function f(z,,

...

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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