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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 critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let Xl Let Xu X2 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics p.d.f. of Yx Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random interval random sample random variables Xl reject H0 respectively sample space Show significance level stochastically independent random subset sufficient statistic testing H0 theorem type of random unbiased statistic variance a2 X2 Xn Xlt X2 Xn denote Xx and X2 zero elsewhere