Introduction to Mathematical Statistics |
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Page 27
... positive integer , n ( a + b ) " = Σ x ! ( n x = 0 n ! x ! ( n − x ) ! b2an — 3 , provided we agree to interpret the symbol 0 ! to be 1. Consider the func- tion defined by f ( x ) = n ! x ! ( n − x ) ! 22 ( 1 − p ) ” — 2 , x = 0 , 1 ...
... positive integer , n ( a + b ) " = Σ x ! ( n x = 0 n ! x ! ( n − x ) ! b2an — 3 , provided we agree to interpret the symbol 0 ! to be 1. Consider the func- tion defined by f ( x ) = n ! x ! ( n − x ) ! 22 ( 1 − p ) ” — 2 , x = 0 , 1 ...
Page 36
... positive number . The integral is called the gamma function of k and we ... integer greater than one , г ( k ) = ( k - 1 ) ( k2 ) ... 3.2.1 ( k - 1 ) ... positive integer , a random variable X having the p.d.f. 1 1 f ( x ) = x2 e 9 0 < x ...
... positive number . The integral is called the gamma function of k and we ... integer greater than one , г ( k ) = ( k - 1 ) ( k2 ) ... 3.2.1 ( k - 1 ) ... positive integer , a random variable X having the p.d.f. 1 1 f ( x ) = x2 e 9 0 < x ...
Page 40
... positive integer n and a number p , 0 < p < 1 ; in the Poisson distribution there was a positive number m , later identified with μ ; in the normal distribu- tion , there were two constants a and b > 0 , later identified with ando ...
... positive integer n and a number p , 0 < p < 1 ; in the Poisson distribution there was a positive number m , later identified with μ ; in the normal distribu- tion , there were two constants a and b > 0 , later identified with ando ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
14 other sections not shown
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