Introduction to Mathematical Statistics |
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Page 53
... compute Pr ( 2 Y ) ; if n = 5 , compute Pr ( 3 ≤ Y ) . ≤ 3.16 . Let Y be the number of successes throughout n independent repetitions of a random experiment having probability of success p = 4. Determine the smallest value of n so ...
... compute Pr ( 2 Y ) ; if n = 5 , compute Pr ( 3 ≤ Y ) . ≤ 3.16 . Let Y be the number of successes throughout n independent repetitions of a random experiment having probability of success p = 4. Determine the smallest value of n so ...
Page 149
... compute Pr ( Y = 48 , 49 , 50 , 51 , 52 ) . Since Y is a random variable of the discrete type , the events Y 47.5 < Y < 52.5 are equivalent . That is , Pr ( Y = < Y < 52.5 ) . Since np written and p = = = = 48 , 49 , 50 , 51 , 52 and ...
... compute Pr ( Y = 48 , 49 , 50 , 51 , 52 ) . Since Y is a random variable of the discrete type , the events Y 47.5 < Y < 52.5 are equivalent . That is , Pr ( Y = < Y < 52.5 ) . Since np written and p = = = = 48 , 49 , 50 , 51 , 52 and ...
Page 162
... computed by using either Equa- tion ( 1 ) or ( 2 ) . By this procedure , suppose it has been found that y = Pr ( Y ; < ¿ p ... Compute Pr ( Y3 < 0.5 < Y7 ) if Y1 < ... < Y , are the order statistics of Y1 a random sample of size 9 from a ...
... computed by using either Equa- tion ( 1 ) or ( 2 ) . By this procedure , suppose it has been found that y = Pr ( Y ; < ¿ p ... Compute Pr ( Y3 < 0.5 < Y7 ) if Y1 < ... < Y , are the order statistics of Y1 a random sample of size 9 from a ...
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