## Introduction to mathematical statistics |

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Page 146

Y25 be two

and n(l, 9), respectively.

Compute Pr (X > Y). n 4.62. Find the mean and variance of S2 = 2 (Xt — X)2/n, ...

Y25 be two

**random**samples from two independent normal distributions «(0, 16)and n(l, 9), respectively.

**Let**X and Y denote the corresponding sample means.Compute Pr (X > Y). n 4.62. Find the mean and variance of S2 = 2 (Xt — X)2/n, ...

Page 153

X10 denote a

Y = 2 (Xi — m)2- What is the probability i that the

includes the point a2? We know that Y/<t2 is x2(10). Moreover, the events ...

X10 denote a

**random**sample of size 10 from a 10 distribution that is n(p, a2).**Let**Y = 2 (Xi — m)2- What is the probability i that the

**random**interval (Y/20.5, Y/3.25)includes the point a2? We know that Y/<t2 is x2(10). Moreover, the events ...

Page 158

It

s2 = 49, s2, = 32, then the interval (-5.16, ...

of a

It

**may**be verified that if in the preceding discussion n = 10, m = 7, x = 4.2, y = 3.4,s2 = 49, s2, = 32, then the interval (-5.16, ...

**Let**the observed value of the mean Xof a

**random**sample of size 20 from a distribution which is n(p, 80) be 81.2.### What people are saying - Write a review

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Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere