Introduction to Mathematical Statistics |
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Page 63
... one or more random variables is called the change of variable technique ... transformation from x to y , and we say that the transformation maps the space A into the space B = { y ; y = 0 , 4 , 8 , 12 , ... } . The space B is obtained by ...
... one or more random variables is called the change of variable technique ... transformation from x to y , and we say that the transformation maps the space A into the space B = { y ; y = 0 , 4 , 8 , 12 , ... } . The space B is obtained by ...
Page 65
... one transformation of A into B. This would enable us to find the joint p.d.f. of Y1 , Y2 , and Ya from which we ... TRANSFORMATIONS OF VARIABLES Transformations of Variables of the Continuous Type.
... one transformation of A into B. This would enable us to find the joint p.d.f. of Y1 , Y2 , and Ya from which we ... TRANSFORMATIONS OF VARIABLES Transformations of Variables of the Continuous Type.
Page 67
... 1 , 0 < x < 1 , = O elsewhere . = We are to show that the random variable Y −2 In X has a chi - square distribu- tion with two degrees of freedom . Here the transformation is y = u ( x ) = -2 ln x , The space A is A = { x ; 0 < x < 1 } ...
... 1 , 0 < x < 1 , = O elsewhere . = We are to show that the random variable Y −2 In X has a chi - square distribu- tion with two degrees of freedom . Here the transformation is y = u ( x ) = -2 ln x , The space A is A = { x ; 0 < x < 1 } ...
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