Introduction to Mathematical Statistics |
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Page 61
... Let X1 , X2 , and X3 denote respectively the number of spades , the number of hearts , and the number of diamonds that appear among the five cards . ( a ) Determine the joint p.d.f. of X1 X2 , and X3 . ( b ) Find the marginal ...
... Let X1 , X2 , and X3 denote respectively the number of spades , the number of hearts , and the number of diamonds that appear among the five cards . ( a ) Determine the joint p.d.f. of X1 X2 , and X3 . ( b ) Find the marginal ...
Page 143
Robert V. Hogg, Allen Thornton Craig. 4.54 . Let X1 , X2 be a random sample from the normal distribution n ( 0 , 1 ) . Let Y X1 + X2 and Z X + X2 . Show that the moment- generating function of the joint distribution of Y and Z is = 1 = E ...
Robert V. Hogg, Allen Thornton Craig. 4.54 . Let X1 , X2 be a random sample from the normal distribution n ( 0 , 1 ) . Let Y X1 + X2 and Z X + X2 . Show that the moment- generating function of the joint distribution of Y and Z is = 1 = E ...
Page 149
... Let X and Y be random variables with μ1 = . Find the mean and variance of Z = 6 , P = 1 , μ2 = 3X 2Y . - = 4 , o ... X1 , X2 , ......... , X2 be a random sample of size n from a distribu- tion with mean μ and variance o2 . Show that E ( S2 ) ...
... Let X and Y be random variables with μ1 = . Find the mean and variance of Z = 6 , P = 1 , μ2 = 3X 2Y . - = 4 , o ... X1 , X2 , ......... , X2 be a random sample of size n from a distribu- tion with mean μ and variance o2 . Show that E ( S2 ) ...
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Common terms and phrases
A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²