## Introduction to mathematical statistics |

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Page 134

Let X1, X2, X3 denote a random sample from the

~x, 0 < x < oo, zero elsewhere. Show that Yl = xT+x,' Y* = x, X+x2X+x3' Y* = X1 +

x* + x* are mutually stochastically independent. 4.37. Let X1, X2, . . . , Xr be r ...

Let X1, X2, X3 denote a random sample from the

**distribution having p.d.f.**f(x) = e~x, 0 < x < oo, zero elsewhere. Show that Yl = xT+x,' Y* = x, X+x2X+x3' Y* = X1 +

x* + x* are mutually stochastically independent. 4.37. Let X1, X2, . . . , Xr be r ...

Page 176

Robert V. Hogg, Allen Thornton Craig. 6.3. Let Yj < Y2 < Y3 be the order statistics

of a random sample of size 3 from the

< oo, zero elsewhere, where — oo < 9 < oo. Determine the function c(8) of 8 so ...

Robert V. Hogg, Allen Thornton Craig. 6.3. Let Yj < Y2 < Y3 be the order statistics

of a random sample of size 3 from the

**distribution having p.d.f.**f(x) = e~{x~e\ 9 < x< oo, zero elsewhere, where — oo < 9 < oo. Determine the function c(8) of 8 so ...

Page 200

Compute an approximate probability that the mean of a random sample of size

15 from a

between f and f. 7.15. Let Y denote the sum of the items of a random sample of

size 12 ...

Compute an approximate probability that the mean of a random sample of size

15 from a

**distribution having p.d.f.**f(x) = 3x2, 0 < x < 1, zero elsewhere, isbetween f and f. 7.15. Let Y denote the sum of the items of a random sample of

size 12 ...

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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