Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 45
Page 36
... integral ( or the n - fold sum , as the case may be ) is called the mathe- matical expectation , denoted by E [ u ... integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
... integral ( or the n - fold sum , as the case may be ) is called the mathe- matical expectation , denoted by E [ u ... integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
Page 96
... integral I = · - S " . exp ( −y2 / 2 ) dy . This integral exists because the integrand is a positive continuous function which is bounded by an integrable function ; that is , 0 < exp ( −y2 / 2 ) < exp ( − | y | + 1 ) , -∞ < y ...
... integral I = · - S " . exp ( −y2 / 2 ) dy . This integral exists because the integrand is a positive continuous function which is bounded by an integrable function ; that is , 0 < exp ( −y2 / 2 ) < exp ( − | y | + 1 ) , -∞ < y ...
Page 344
... integral - μ 4 ) A ( x — H ) ] da , t1 , t2 , · .. ) ( 2 ) C cf ... [ exp [ t'x . ∞ ( x - - and then we shall subsequently set t1 = t2 xn 2 = ... dx1 dxn , ... = tn = 0 , and thus establish Equation ( 1 ) . First we change the ...
... integral - μ 4 ) A ( x — H ) ] da , t1 , t2 , · .. ) ( 2 ) C cf ... [ exp [ t'x . ∞ ( x - - and then we shall subsequently set t1 = t2 xn 2 = ... dx1 dxn , ... = tn = 0 , and thus establish Equation ( 1 ) . First we change the ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²