## Introduction to Mathematical Statistics |

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Page 54

obtain more information about this distribution (or the unknown parameter), we

shall repeat under identical conditions the ... The random variables X1, X2, ..., Xn

are then said to constitute a random sample from a

obtain more information about this distribution (or the unknown parameter), we

shall repeat under identical conditions the ... The random variables X1, X2, ..., Xn

are then said to constitute a random sample from a

**distribution having p.d.f.**f(z).Page 57

Find the probability that exactly four items of a random sample of size 5 from the

• 3.26. Let X1, X2, Xs be a random sample of size 3 from a normal distribution ...

Find the probability that exactly four items of a random sample of size 5 from the

**distribution having p.d.f.**f(z) = (x + 1)/2, — 1 < z < 1, zero elsewhere, exceed zero.• 3.26. Let X1, X2, Xs be a random sample of size 3 from a normal distribution ...

Page 156

Accordingly the joint

co, 0 < 2, 3 co, = 0 elsewhere. ... Let Y, & Y2 < Ys 3 Y. 3 Ys denote the order

statistics of a random sample of size 5 from a

...

Accordingly the joint

**p.d.f.**of Zi and Z2 is h(zi,z) = 120e “(1 – e')e”(1 – e'), 0 < 2, 3co, 0 < 2, 3 co, = 0 elsewhere. ... Let Y, & Y2 < Ys 3 Y. 3 Ys denote the order

statistics of a random sample of size 5 from a

**distribution having**the**p.d. f.**f(z) = 1,...

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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