Introduction to Mathematical Statistics |
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Page 48
... result tell us what the p.d.f. g ( y ) of Y is . Now the moment- generating function of Y is My ( t ) = E [ e " ( x1 + x , ) ] = = E ( ex ) E ( ex ) E ( ex ) since X1 and X2 are stochastically independent . In this example X1 and X2 ...
... result tell us what the p.d.f. g ( y ) of Y is . Now the moment- generating function of Y is My ( t ) = E [ e " ( x1 + x , ) ] = = E ( ex ) E ( ex ) E ( ex ) since X1 and X2 are stochastically independent . In this example X1 and X2 ...
Page 66
... result by the derivative of ( 1⁄2 ) Vy . That is , o ( u ) = f ( Vi ) d [ ( 3 ) vū ] g ( g ) 2 = 0 elsewhere . dy = 1 - 0 < y < 8 , 6y1 / 3 We shall accept a theorem in analysis on the change of variable in a definite integral to enable ...
... result by the derivative of ( 1⁄2 ) Vy . That is , o ( u ) = f ( Vi ) d [ ( 3 ) vū ] g ( g ) 2 = 0 elsewhere . dy = 1 - 0 < y < 8 , 6y1 / 3 We shall accept a theorem in analysis on the change of variable in a definite integral to enable ...
Page 214
... result obtained will be non - negative . This result is ∞ ∞ SS [ ( u - - ( y — μ2 ) — p22 ( x − μ1 ) f ( x , y ) dy dx με ) = SS [ μι ) ( 3 —μ2 ) 2 — 2,032 ( y — μ2 ) ( x — μs ) +2012 ( x − μ41 ) 2 σι = E [ ( Y — μ2 ) 2 ] — 2 p2 2 E ...
... result obtained will be non - negative . This result is ∞ ∞ SS [ ( u - - ( y — μ2 ) — p22 ( x − μ1 ) f ( x , y ) dy dx με ) = SS [ μι ) ( 3 —μ2 ) 2 — 2,032 ( y — μ2 ) ( x — μs ) +2012 ( x − μ41 ) 2 σι = E [ ( Y — μ2 ) 2 ] — 2 p2 2 E ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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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