## Introduction to Mathematical Statistics |

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Page 20

This sum of products is seen to be a “weighted average” of the

..., the “weight” associated with each as being f(a). This suggests that we call E(X)

the arithmetic mean of the

This sum of products is seen to be a “weighted average” of the

**values**a1, a2, a3,..., the “weight” associated with each as being f(a). This suggests that we call E(X)

the arithmetic mean of the

**values**of X, or, more simply, the mean**value**of X (or ...Page 48

Then the table g 2 3 4 5 6 TTTIOTT2-5 7(9)|35 33 35 § 3; gives the

for y = 2, 3, 4, 5, 6. For all other

is to define a new random variable Y by Y = XI + X2, and we have found the p.a.f.

...

Then the table g 2 3 4 5 6 TTTIOTT2-5 7(9)|35 33 35 § 3; gives the

**values**of g(y)for y = 2, 3, 4, 5, 6. For all other

**values**of y, g(y) = 0. What we have actually doneis to define a new random variable Y by Y = XI + X2, and we have found the p.a.f.

...

Page 205

The constant c is so selected as to yield the desired

If in the preceding discussion a = 4 and b = 3, test at the 5 per cent significance

level the null hypothesis 81 = 82 = 83 - 0 if the observed

The constant c is so selected as to yield the desired

**value**of oz. Exercises • 10.7.If in the preceding discussion a = 4 and b = 3, test at the 5 per cent significance

level the null hypothesis 81 = 82 = 83 - 0 if the observed

**values**of Xi, are 3 5 7 ...### What people are saying - Write a review

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere