Introduction to Mathematical Statistics |
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Page 37
... expected value of the length X is E ( X ) = 1⁄2 and the expected value of the length 5 X is E ( 5 X ) = 2. But the expected value of the product of the two lengths is equal to 5 E [ X ( 5 − X ) ] = √® x ( 5 - 0 - x ) ( 3 ) dx 25 = # 6 ...
... expected value of the length X is E ( X ) = 1⁄2 and the expected value of the length 5 X is E ( 5 X ) = 2. But the expected value of the product of the two lengths is equal to 5 E [ X ( 5 − X ) ] = √® x ( 5 - 0 - x ) ( 3 ) dx 25 = # 6 ...
Page 72
... expected value of the product of a function u ( X1 ) of X1 alone and a function v ( X2 ) of X2 alone is , subject to their existence , equal to the product of the expected value of u ( X1 ) and the expected value of v ( X2 ) ; that is ...
... expected value of the product of a function u ( X1 ) of X1 alone and a function v ( X2 ) of X2 alone is , subject to their existence , equal to the product of the expected value of u ( X1 ) and the expected value of v ( X2 ) ; that is ...
Page 153
... expected value of the length of the random interval is 2.602 . EXERCISES = = 5.1 . Let the random variable X have the p.d.f. f ( x ) e - x , 0 < x < ∞∞ , zero elsewhere . Compute the probability that the random interval ( X , 3X ) ...
... expected value of the length of the random interval is 2.602 . EXERCISES = = 5.1 . Let the random variable X have the p.d.f. f ( x ) e - x , 0 < x < ∞∞ , zero elsewhere . Compute the probability that the random interval ( X , 3X ) ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ