Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 35
Page 73
... p.d.f. ƒ1 ( x1 ) ƒ2 ( x2 ) that is positive on the two - dimensional space A ... marginal probability density functions of Y1 and Y2 are respectively g1 ( y1 ) ... p.d.f. f ( x ) = x2 / 9 , 0 < x < 3 , zero elsewhere . Find the p.d.f. of Y ...
... p.d.f. ƒ1 ( x1 ) ƒ2 ( x2 ) that is positive on the two - dimensional space A ... marginal probability density functions of Y1 and Y2 are respectively g1 ( y1 ) ... p.d.f. f ( x ) = x2 / 9 , 0 < x < 3 , zero elsewhere . Find the p.d.f. of Y ...
Page 94
... p.d.f. and a conditional expectation . Let f ( x1 , x2 , ...... , Xn ) be the joint p.d.f. of the n random variables X1 , X2 , ... , Xn . Let fi ( x1 ) , ƒ2 ( X2 ) , ... , fn ( xn ) be respec- tively the ( one variable ) marginal ...
... p.d.f. and a conditional expectation . Let f ( x1 , x2 , ...... , Xn ) be the joint p.d.f. of the n random variables X1 , X2 , ... , Xn . Let fi ( x1 ) , ƒ2 ( X2 ) , ... , fn ( xn ) be respec- tively the ( one variable ) marginal ...
Page 218
... marginal p.d.f. that is n ( u ; 0 , 1 ) . In like manner , the marginal p.d.f. of V is n ( v ; 0 , 1 ) . Let us define the random variables X and Y by U = X b ― a Y b > 0 , and V. = = c , d > 0 . d = 0 and E ( U2 ) = E ( V2 ) = 1 , then ...
... marginal p.d.f. that is n ( u ; 0 , 1 ) . In like manner , the marginal p.d.f. of V is n ( v ; 0 , 1 ) . Let us define the random variables X and Y by U = X b ― a Y b > 0 , and V. = = c , d > 0 . d = 0 and E ( U2 ) = E ( V2 ) = 1 , then ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
14 other sections not shown
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