Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 91
Page 18
... , be the p.d.f. of X. Find Pr [ X = 1 or 2 ] , Pr [ < X < ] , and Pr [ 1 ≤ X ≤ 2 ] . 1.29 . Let f ( x ) = 1 / x2 , 1 < x < ∞o , A1 = { x ; 1 < x < 2 } and A2 = { x ; P ( A1A2 ) . 1.30 . Let f ( x1 , x2 ) = zero elsewhere , be the p.d.f. ...
... , be the p.d.f. of X. Find Pr [ X = 1 or 2 ] , Pr [ < X < ] , and Pr [ 1 ≤ X ≤ 2 ] . 1.29 . Let f ( x ) = 1 / x2 , 1 < x < ∞o , A1 = { x ; 1 < x < 2 } and A2 = { x ; P ( A1A2 ) . 1.30 . Let f ( x1 , x2 ) = zero elsewhere , be the p.d.f. ...
Page 25
... X to be a random variable of the discrete or continuous type . and ( a ) 0 ≤ F ( x ) ≤ 1 because 0 ≤ Pr ( X ≤ x ) ≤ 1 . ( b ) F ( x ) is a nondecreasing function of x . For , if x ' < x " , then That is , { x ; x ≤ x " } = { x ; x ≤ ...
... X to be a random variable of the discrete or continuous type . and ( a ) 0 ≤ F ( x ) ≤ 1 because 0 ≤ Pr ( X ≤ x ) ≤ 1 . ( b ) F ( x ) is a nondecreasing function of x . For , if x ' < x " , then That is , { x ; x ≤ x " } = { x ; x ≤ ...
Page 94
... ( x ) of this form is called a chi - square p.d.f. The mean and the variance of a chi - square distribution are μ = aß ... Pr ( X Pr ( c1 ≤ X ≤ c2 ) = Pr ( X ≤ c2 ) - Pr ( X ≤ c1 ) , = C1 ) c1 ) = 0. To compute such a probability , we ...
... ( x ) of this form is called a chi - square p.d.f. The mean and the variance of a chi - square distribution are μ = aß ... Pr ( X Pr ( c1 ≤ X ≤ c2 ) = Pr ( X ≤ c2 ) - Pr ( X ≤ c1 ) , = C1 ) c1 ) = 0. To compute such a probability , we ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider 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 H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions 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 theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ