## Introduction to Mathematical Statistics |

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Page 57

Find the probability that exactly four items of a

distribution having p.d.f. f(z) = (x + 1)/2, — 1 < z < 1, zero elsewhere, exceed zero.

• 3.26.

Find the probability that exactly four items of a

**random**sample of size 5 from thedistribution 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 130

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normal distributions n(z; ul, alo) and n(y; us, go”), respectively. The four

parameters ul, u2, oi", a 2° are unknown, but at the moment we have no concern

with ul and ...

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**let**X and Y denote stochastically independent**random**variables havingnormal distributions n(z; ul, alo) and n(y; us, go”), respectively. The four

parameters ul, u2, oi", a 2° are unknown, but at the moment we have no concern

with ul and ...

Page 182

9. 18.

distribution n(z; 6, 100). Find a uniformly most powerful critical region of size a =

0.10 for testing Ho: 6 = 75 against H1: 9 × 75. 9.19.

9. 18.

**Let**X1, X2, ..., Xas denote a**random**sample of size 25 from a normaldistribution n(z; 6, 100). Find a uniformly most powerful critical region of size a =

0.10 for testing Ho: 6 = 75 against H1: 9 × 75. 9.19.

**Let**X1, X2, ..., Xn denote a**random**...### What people are saying - Write a review

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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