Introduction to Mathematical Statistics |
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Page 27
... distributions arise or how they are used . We wish primarily to establish their names and some of their properties . 2.1 . Two Discrete - Type Distributions . In this section we introduce the binomial and Poisson distributions . ( a ) The ...
... distributions arise or how they are used . We wish primarily to establish their names and some of their properties . 2.1 . Two Discrete - Type Distributions . In this section we introduce the binomial and Poisson distributions . ( a ) The ...
Page 144
... distribution , namely , the Poisson dis- tribution with mean μ , that has this moment - generating function ( e − 1 ) ... binomial distribution when ʼn is large and p is small . This is clearly an advantage for it is easy to provide ...
... distribution , namely , the Poisson dis- tribution with mean μ , that has this moment - generating function ( e − 1 ) ... binomial distribution when ʼn is large and p is small . This is clearly an advantage for it is easy to provide ...
Page 149
... binomial distribution with param- eters n and p . Calculation of probabilities concerning Y , when we do not use the Poisson approximation , can be greatly simplified by making use of the fact that ( Y - np ) / √np ( 1 - p ) √n ( x ...
... binomial distribution with param- eters n and p . Calculation of probabilities concerning Y , when we do not use the Poisson approximation , can be greatly simplified by making use of the fact that ( Y - np ) / √np ( 1 - p ) √n ( x ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²