## Introduction to Mathematical Statistics |

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Page 161

It is interesting to observe that the right-hand member of

obtained by a more direct argument. If we are to have Yo 3 #2, at least k items of

the random sample must be less than £p. Now Pr(X & #2) = p, where X is an item

of ...

It is interesting to observe that the right-hand member of

**equation**(2) can beobtained by a more direct argument. If we are to have Yo 3 #2, at least k items of

the random sample must be less than £p. Now Pr(X & #2) = p, where X is an item

of ...

Page 201

... expression (1), is set equal to zero, the solution for u is -- ~ * >, 1 b o o QM, is

ão 2 rif. j=1 is 1 If the partial derivatives, expression (3), are equated to zero, we

have b b (5) XXros – bas – XXros -- bo. = 0, i = 1, 2, ..., a -1. j=1 j= 1

is ...

... expression (1), is set equal to zero, the solution for u is -- ~ * >, 1 b o o QM, is

ão 2 rif. j=1 is 1 If the partial derivatives, expression (3), are equated to zero, we

have b b (5) XXros – bas – XXros -- bo. = 0, i = 1, 2, ..., a -1. j=1 j= 1

**Equation**(5)is ...

Page 213

If both members of

X), Or (2) pu2 = 0. + bul, where ui = E(X) and u2 = E(Y). If both members of

E(X) ...

If both members of

**Equation**(1) are integrated on 2, it is seen that E(Y) = a + b E(X), Or (2) pu2 = 0. + bul, where ui = E(X) and u2 = E(Y). If both members of

**Equation**(1) are first multiplied by a and then integrated on 2, we have E(X|Y) = aE(X) ...

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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