Introduction to Mathematical Statistics |
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Page 29
... Poisson distribution . Recall that the series m2 m3 1 + m + + + 2 ! 3 ! converges , for all values of m , to em . f ( x ) = me - m x ! = ... mx x ! Ση Consider the function f ( x ) defined by x = 0 , 1 , 2 , ... = 0 elsewhere , where m ...
... Poisson distribution . Recall that the series m2 m3 1 + m + + + 2 ! 3 ! converges , for all values of m , to em . f ( x ) = me - m x ! = ... mx x ! Ση Consider the function f ( x ) defined by x = 0 , 1 , 2 , ... = 0 elsewhere , where m ...
Page 30
... Poisson distribution has μ = σ2 = m > 0. On this account , a Poisson p.d.f. is frequently written f ( x ) = кретн x ! x = 0 , 1 , 2 , ... = O elsewhere . EXAMPLE 3. Suppose X has a Poisson distribution with μ = 2. Then the p.d.f. of X ...
... Poisson distribution has μ = σ2 = m > 0. On this account , a Poisson p.d.f. is frequently written f ( x ) = кретн x ! x = 0 , 1 , 2 , ... = O elsewhere . EXAMPLE 3. Suppose X has a Poisson distribution with μ = 2. Then the p.d.f. of X ...
Page 144
... Poisson dis- tribution with mean μ , that has this moment - generating function ( e − 1 ) , then in accordance with the theorem and under the conditions stated , it is seen that Y has a limiting Poisson distribution ... distribution , we may ...
... Poisson dis- tribution with mean μ , that has this moment - generating function ( e − 1 ) , then in accordance with the theorem and under the conditions stated , it is seen that Y has a limiting Poisson distribution ... distribution , we may ...
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