Introduction to Mathematical Statistics |
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Page 21
... note that if the sample space contains only one point x for which f ( x ) > 0 , then σ = 0 . Comment . Let the random variable X of the continuous type have the p.d.f. f ( x ) = 1 / ( 2a ) , -a < x < a , zero elsewhere , so that σ = a ...
... note that if the sample space contains only one point x for which f ( x ) > 0 , then σ = 0 . Comment . Let the random variable X of the continuous type have the p.d.f. f ( x ) = 1 / ( 2a ) , -a < x < a , zero elsewhere , so that σ = a ...
Page 63
... note two things about this transformation : It is such that to each point in A there corresponds one , and only one ... note that a one - to - one tranformation , y = u ( x ) , implies that y is a single - valued func- tion of x , and ...
... note two things about this transformation : It is such that to each point in A there corresponds one , and only one ... note that a one - to - one tranformation , y = u ( x ) , implies that y is a single - valued func- tion of x , and ...
Page 189
... Note that there are only two points in 2 . n 9.24 . Verify equations ( 1 ) of Example 2 of this section . 9.25 . Verify equations ( 2 ) of Example 2 of this section . 9.26 . Let X1 , X2 , *** , X , be a random sample from the normal ...
... Note that there are only two points in 2 . n 9.24 . Verify equations ( 1 ) of Example 2 of this section . 9.25 . Verify equations ( 2 ) of Example 2 of this section . 9.26 . Let X1 , X2 , *** , X , be a random sample from the normal ...
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