Introduction to Mathematical Statistics |
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Page 34
... Compute the probability that this person will win at least one prize . 1.48 . Compute the probability of being dealt at random and without replacement a 13 - card bridge hand consisting of : ( a ) 6 spades , 4 hearts , 2 diamonds , and ...
... Compute the probability that this person will win at least one prize . 1.48 . Compute the probability of being dealt at random and without replacement a 13 - card bridge hand consisting of : ( a ) 6 spades , 4 hearts , 2 diamonds , and ...
Page 54
... compute the probability that there is at least one matching pair among these six socks . Hint . Compute the probability that there is not a matching pair . 2.6 . A bowl contains ten chips . Four of the chips are red , five are white ...
... compute the probability that there is at least one matching pair among these six socks . Hint . Compute the probability that there is not a matching pair . 2.6 . A bowl contains ten chips . Four of the chips are red , five are white ...
Page 182
... Compute ( a ) Pr ( Y1 < 0.5 < Y5 ) ; 1 ( b ) Pr ( Y1 < $ 0.25 < Y3 ) ; 1 ( c ) Pr ( Y4 < $ 0.80 < Y5 ) . 1 9 6.17 . Compute Pr ( Y3 < 0.5 < Y1 ) if Y1 < ... < Y , are the order statistics of a random sample of size 9 from a distribution ...
... Compute ( a ) Pr ( Y1 < 0.5 < Y5 ) ; 1 ( b ) Pr ( Y1 < $ 0.25 < Y3 ) ; 1 ( c ) Pr ( Y4 < $ 0.80 < Y5 ) . 1 9 6.17 . Compute Pr ( Y3 < 0.5 < Y1 ) if Y1 < ... < Y , are the order statistics of a random sample of size 9 from a distribution ...
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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