## Introduction to Mathematical Statistics |

### From inside the book

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Page 48

This suggests that we can first find the moment-generating function of Y = X1 +

X2 and let this

function of Y is My(t) = Ele”) = E(e”e”) = E(e”).E(e”) since X1 and X2 are ...

This suggests that we can first find the moment-generating function of Y = X1 +

X2 and let this

**result**tell us what the p.d.f. g(y) of Y is. Now the momentgeneratingfunction of Y is My(t) = Ele”) = E(e”e”) = E(e”).E(e”) since X1 and X2 are ...

Page 66

0 < y < 8, We shall accept a theorem in analysis on the change of variable in a

definite integral to enable us to state a more general

variable of the continuous type having p.d.f. f(z). Let A be the one-dimensional

space ...

0 < y < 8, We shall accept a theorem in analysis on the change of variable in a

definite integral to enable us to state a more general

**result**. Let X be a randomvariable of the continuous type having p.d.f. f(z). Let A be the one-dimensional

space ...

Page 214

This variance is non-negative and is at most a function of z alone. If then, it is

multiplied by f(z) and integrated on 2, the

This

da.

This variance is non-negative and is at most a function of z alone. If then, it is

multiplied by f(z) and integrated on 2, the

**result**obtained will be non-negative.This

**result**is oo co 2 s s so – u2) — o - ofte y) dy da: -so so so-o-o-o-o-o-o: y) dyda.

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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