Introduction to Mathematical Statistics |
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Page 25
... show that this series converges only if t≤0 . Thus there does not exist a positive number h such that Mx ( t ) ... show that E ( X2 ) 1.39 . Let a random variable X of the continuous type have a p.d.f. f ( x ) whose graph is symmetric ...
... show that this series converges only if t≤0 . Thus there does not exist a positive number h such that Mx ( t ) ... show that E ( X2 ) 1.39 . Let a random variable X of the continuous type have a p.d.f. f ( x ) whose graph is symmetric ...
Page 31
... Show that 5 9 ! Pr ( u – 20 < x < μ + 20 ) = Σ1 ( 2o ± 21 ( 3 ) * ( 3 ) ̃ * - x ! ( 9 ( 2.5 . Let X have a binomial distribution . Show that and np √np ( 1 — p ) E ( XMP ) -0 , = = np E [ ( X - 2 ) ] - 1 , np ( 1 p ) . = B [ e ...
... Show that 5 9 ! Pr ( u – 20 < x < μ + 20 ) = Σ1 ( 2o ± 21 ( 3 ) * ( 3 ) ̃ * - x ! ( 9 ( 2.5 . Let X have a binomial distribution . Show that and np √np ( 1 — p ) E ( XMP ) -0 , = = np E [ ( X - 2 ) ] - 1 , np ( 1 p ) . = B [ e ...
Page 104
... Show that X , is a sufficient statistic for 0 . 5.15 . Prove that the sum of the items of a random sample of size n from a Poisson distribution having parameter 0 , 0 < 0 < ∞ , is a sufficient statistic for 0 . 5.16 . Show that the nth ...
... Show that X , is a sufficient statistic for 0 . 5.15 . Prove that the sum of the items of a random sample of size n from a Poisson distribution having parameter 0 , 0 < 0 < ∞ , is a sufficient statistic for 0 . 5.16 . Show that the nth ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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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