Introduction to Mathematical Statistics |
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Page 12
... discrete type , and X is said to have a distribution of the discrete type . EXAMPLE 1. Let X be a random variable of the discrete type with sample space A = { x ; x = 0 , 1 , 2 , 3 , 4 } . Let P ( A ) = Σf ( x ) , where 4 ! f ( x ) = xd ...
... discrete type , and X is said to have a distribution of the discrete type . EXAMPLE 1. Let X be a random variable of the discrete type with sample space A = { x ; x = 0 , 1 , 2 , 3 , 4 } . Let P ( A ) = Σf ( x ) , where 4 ! f ( x ) = xd ...
Page 14
... discrete type or of the continuous type , and have a distribution of that type , according as the probability set func- tion P ( A ) , A CA , is defined by P ( A ) = Pr [ ( X , Y ) εA ] = ΣΣΙ ( x , y ) , or by P ( A ) = Pr [ ( X , Y ) ...
... discrete type or of the continuous type , and have a distribution of that type , according as the probability set func- tion P ( A ) , A CA , is defined by P ( A ) = Pr [ ( X , Y ) εA ] = ΣΣΙ ( x , y ) , or by P ( A ) = Pr [ ( X , Y ) ...
Page 63
... a random variable of the discrete type , having p.d.f. f ( x ) . Let A denote the set of discrete points , at each of which f ( x ) > 0 , and let y $ 4.1 ] TRANSFORMATIONS OF VARIABLES 63 Transformations of Variables of the Discrete Type.
... a random variable of the discrete type , having p.d.f. f ( x ) . Let A denote the set of discrete points , at each of which f ( x ) > 0 , and let y $ 4.1 ] TRANSFORMATIONS OF VARIABLES 63 Transformations of Variables of the Discrete Type.
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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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