## Introduction to Mathematical Statistics |

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Whenever a probability set function P(A), A C A, is defined in terms of such an f(z)

by P(A) = Pr(XeA) = X f(x), then X is called a random variable of the

and X is said to have a distribution of the

Whenever a probability set function P(A), A C A, is defined in terms of such an f(z)

by P(A) = Pr(XeA) = X f(x), then X is called a random variable of the

**discrete type**,and X is said to have a distribution of the

**discrete type**. ExAMPLE 1. Let X be a ...Page 14

tions which will not be enumerated here), we say that the two random variables X

and Y are of the

that type, according as the probability set function P(A), A C A, is defined by ...

tions which will not be enumerated here), we say that the two random variables X

and Y are of the

**discrete type**or of the continuous type, and have a distribution ofthat type, according as the probability set function P(A), A C A, is defined by ...

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Transformations of Variables of the

finding the distribution of a function of one or more random variables is called the

change of variable technique. There are some delicate questions (with particular

...

Transformations of Variables of the

**Discrete Type**. An alternative method offinding the distribution of a function of one or more random variables is called the

change of variable technique. There are some delicate questions (with particular

...

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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