Introduction to Mathematical Statistics |
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Page 194
... ( Exercise 10.1 ) that Q3 / 02 has a chi - square distribution with b ( a - 1 ) degrees of freedom . Since Q1 = aΣ ( X ... Exercises 10.1 . In Example 2 , verify that Q = Q3 Q4 and that Q3 / 02 has a chi - square distribution with b ( a 1 ) ...
... ( Exercise 10.1 ) that Q3 / 02 has a chi - square distribution with b ( a - 1 ) degrees of freedom . Since Q1 = aΣ ( X ... Exercises 10.1 . In Example 2 , verify that Q = Q3 Q4 and that Q3 / 02 has a chi - square distribution with b ( a 1 ) ...
Page 205
... Exercises 10.7 . If in the preceding discussion a = 4 and b significance level the null hypothesis Bi Xi , are = 3 ... Exercise 10.7 to test at the 5 per cent significance level the null hypothesis in Exercise 10.10 . X10.12 . Let the ...
... Exercises 10.7 . If in the preceding discussion a = 4 and b significance level the null hypothesis Bi Xi , are = 3 ... Exercise 10.7 to test at the 5 per cent significance level the null hypothesis in Exercise 10.10 . X10.12 . Let the ...
Page 220
... Exercises 11.1 ( c ) and 11.10 , page 216. The importance of the theorem lies in the fact that we now know when , and only when , two random variables having a bivariate normal distribution are stochastically independent . Exercises ...
... Exercises 11.1 ( c ) and 11.10 , page 216. The importance of the theorem lies in the fact that we now know when , and only when , two random variables having a bivariate normal distribution are stochastically independent . Exercises ...
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