Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 20
Page 79
... binomial distribution , and any such f ( x ) is called a binomial p.d.f. A binomial distribution will be denoted by the symbol b ( n , p ) . The constants n and p are called the parameters of the binomial distribution . Thus , if we say ...
... binomial distribution , and any such f ( x ) is called a binomial p.d.f. A binomial distribution will be denoted by the symbol b ( n , p ) . The constants n and p are called the parameters of the binomial distribution . Thus , if we say ...
Page 194
... distribution of the binomial distribution , when = = p = u / n , by finding the limit of M ( t ; n ) . Now M ( t ; n ) = E ( etx ) = [ ( 1 − p ) + pet ] n = [ 1 μlet 1 + = 1 ) ] " - n for all real values of t . Hence , we have lim M ...
... distribution of the binomial distribution , when = = p = u / n , by finding the limit of M ( t ; n ) . Now M ( t ; n ) = E ( etx ) = [ ( 1 − p ) + pet ] n = [ 1 μlet 1 + = 1 ) ] " - n for all real values of t . Hence , we have lim M ...
Page 379
... distribution ( s ) , chi- square , 300 normal for binomial , 199 normal for chi - square , 194 normal for Poisson , 195 of X , 196 , 198 Poisson for binomial , 194 Bayes ' formula , 54 Bayesian statistics , 164 , 251 , 279 , 282 , 283 ...
... distribution ( s ) , chi- square , 300 normal for binomial , 199 normal for chi - square , 194 normal for Poisson , 195 of X , 196 , 198 Poisson for binomial , 194 Bayes ' formula , 54 Bayesian statistics , 164 , 251 , 279 , 282 , 283 ...
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