Introduction to Mathematical Statistics |
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Page 19
... constant , then E ( k ) = K. This follows from expression ( 1 ) [ or ( 2 ) ] upon setting u = k and recalling that an integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
... constant , then E ( k ) = K. This follows from expression ( 1 ) [ or ( 2 ) ] upon setting u = k and recalling that an integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
Page 40
... constants a and b > 0 , later identified with ando , respectively ; and in the chi - square distribution a positive integer r , which was called the number of degrees of freedom of the chi - square distribution . Any such constant which ...
... constants a and b > 0 , later identified with ando , respectively ; and in the chi - square distribution a positive integer r , which was called the number of degrees of freedom of the chi - square distribution . Any such constant which ...
Page 121
... constant , so that each of the functions L and g1 [ u1 ( x1 , x2 , ... , Xn ) ; 0 ] is a maximum simultaneously . Apart from trivial solutions ( that is , a constant ) any @ that maximizes 91 [ U1 ( X1 , X2 , ... , Xn ) ; 0 ] will be a ...
... constant , so that each of the functions L and g1 [ u1 ( x1 , x2 , ... , Xn ) ; 0 ] is a maximum simultaneously . Apart from trivial solutions ( that is , a constant ) any @ that maximizes 91 [ U1 ( X1 , X2 , ... , Xn ) ; 0 ] will be a ...
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