Introduction to Mathematical Statistics |
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Page 54
... distribution under consideration . Comments . Let it be assumed that the ... p.d.f. f ( x ) ; that is , the probability density functions of X1 , X2 ... having p.d.f. f ( x ) . Sometimes it is convenient to refer to a random sample of ...
... distribution under consideration . Comments . Let it be assumed that the ... p.d.f. f ( x ) ; that is , the probability density functions of X1 , X2 ... having p.d.f. f ( x ) . Sometimes it is convenient to refer to a random sample of ...
Page 55
... p.d.f. of the sum Y X1 + X2 + + Xn of the n items of the random sample . And in the latter part of Example 5 we investigated some of the properties of the distribution ... having p.d.f. f ( x ) . Certain functions of the items of a random ...
... p.d.f. of the sum Y X1 + X2 + + Xn of the n items of the random sample . And in the latter part of Example 5 we investigated some of the properties of the distribution ... having p.d.f. f ( x ) . Certain functions of the items of a random ...
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... distribution having p.d.f. f ( x ) ( x + 1 ) / 2 , −1 < x < 1 , zero else- where , exceed zero . = - 3.26 . Let X1 , X2 , X3 be a random sample of size 3 from a normal distribution n ( x ; 6 , 4 ) . Determine the probability that the ...
... distribution having p.d.f. f ( x ) ( x + 1 ) / 2 , −1 < x < 1 , zero else- where , exceed zero . = - 3.26 . Let X1 , X2 , X3 be a random sample of size 3 from a normal distribution n ( x ; 6 , 4 ) . Determine the probability that the ...
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