Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 114
... Let the random variable X , be equal to the number of spots that appear on the ith trial , i = 1 , 2 , 3. Let the random variable Y be equal to max ( X ) . Find the distribution function and the p.d.f. of Y. Hint : Pr ( Y≤ y ) = Pr ( X ...
... Let the random variable X , be equal to the number of spots that appear on the ith trial , i = 1 , 2 , 3. Let the random variable Y be equal to max ( X ) . Find the distribution function and the p.d.f. of Y. Hint : Pr ( Y≤ y ) = Pr ( X ...
Page 125
... Let X have a binomial distribution with parameters n and p = . Determine the smallest integer n can be such that Pr ... random experiment be repeated five independent times . Let the random variable X , be the number of terminations in ...
... Let X have a binomial distribution with parameters n and p = . Determine the smallest integer n can be such that Pr ... random experiment be repeated five independent times . Let the random variable X , be the number of terminations in ...
Page 156
Robert V. Hogg, Allen Thornton Craig. let the random variables X , i = 1 , 2 , ... , n , be independent , each having the same p.d.f. f ( x ) = p ( 1 − p ) 1 ̄ * , x = 0 , 1 , and zero else- n where . If Y = X1 , then Y is b ( n , p ) ...
Robert V. Hogg, Allen Thornton Craig. let the random variables X , i = 1 , 2 , ... , n , be independent , each having the same p.d.f. f ( x ) = p ( 1 − p ) 1 ̄ * , x = 0 , 1 , and zero else- n where . If Y = X1 , then Y is b ( n , p ) ...
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Common terms and phrases
A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²