## Introduction to Mathematical Statistics |

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Page 85

given by ssJoey(2:2)f(x3) dzi dao da's = 0, since f(z) dzi is defined in calculus to

be zero. As in the latter part of the preceding section we may, without altering the

...

**Consider**a probability such as Pr(a 3 X = X2 < b, a 3 X, < b). This probability isgiven by ssJoey(2:2)f(x3) dzi dao da's = 0, since f(z) dzi is defined in calculus to

be zero. As in the latter part of the preceding section we may, without altering the

...

Page 178

page 169. It is desired to test the null simple hypothesis Ho: 6 = 2 against the

alternative composite hypothesis H1: 6 × 2. A random sample X1, X2 of size n = 2

will ...

**Consider**the p.d.f. 1 — f(x, 0) = #e , 0 < r < co, ; = 0 elsewhere, of Example 2,page 169. It is desired to test the null simple hypothesis Ho: 6 = 2 against the

alternative composite hypothesis H1: 6 × 2. A random sample X1, X2 of size n = 2

will ...

Page 192

Let the random variable X have a distribution that is n(z; u, o”). Let a and b denote

positive integers greater than one and let n = ab.

size n = ab from this normal distribution. The items of the random sample will be ...

Let the random variable X have a distribution that is n(z; u, o”). Let a and b denote

positive integers greater than one and let n = ab.

**Consider**a random sample ofsize n = ab from this normal distribution. The items of the random sample will be ...

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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