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Page 139
... one . Exercises = - 6x ( 1 − x ) , 0 < x < 1 , zero 7.1 . Let X have a distribution with p.d.f. f ( x ) elsewhere . Find the distribution function F ( x ) of X , 7.2 . If X has the p.d.f. f ( x 87.1 ] 139 THE DISTRIBUTION FUNCTION.
... one . Exercises = - 6x ( 1 − x ) , 0 < x < 1 , zero 7.1 . Let X have a distribution with p.d.f. f ( x ) elsewhere . Find the distribution function F ( x ) of X , 7.2 . If X has the p.d.f. f ( x 87.1 ] 139 THE DISTRIBUTION FUNCTION.
Page 140
... Distributions . In the introduction to this chapter there were described certain random variables whose distributions depend upon the sample size n . Clearly the distribution function F that corresponds to each of these distributions ...
... Distributions . In the introduction to this chapter there were described certain random variables whose distributions depend upon the sample size n . Clearly the distribution function F that corresponds to each of these distributions ...
Page 142
... distribution . However , the distribution function of X is Fn ( ) = 0 , a < 2+ 1 1 = 1 , x ≥ 2 + 1 , and lim F ( x ) = 0 , x ≤ 2 , ∞4u = 1 , x > 2 . Since F ( x ) = 0 , x < 2 , = = 1 , x ≥ 2 , is a distribution function , and since ...
... distribution . However , the distribution function of X is Fn ( ) = 0 , a < 2+ 1 1 = 1 , x ≥ 2 + 1 , and lim F ( x ) = 0 , x ≤ 2 , ∞4u = 1 , x > 2 . Since F ( x ) = 0 , x < 2 , = = 1 , x ≥ 2 , is a distribution function , and since ...
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