## Introduction to Mathematical Statistics |

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Page 13

ca” da = 1, 0 It is seen that whether the random variable X is of the discrete type

or of the

function f(z). In either case f(z) is called the probability density function (hereafter

...

ca” da = 1, 0 It is seen that whether the random variable X is of the discrete type

or of the

**continuous type**, the probability Pr(XeA) is completely determined by afunction f(z). In either case f(z) is called the probability density function (hereafter

...

Page 14

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

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 ...

Page 15

Similarly, after extending the definition of a p.d.f. of the discrete type, we replace,

for one random variable, Xi(x) by X's.), ... If f(z) is the p.c.f. of a

random variable X and if A is the set {z; a 3 a < b%, then P(A) = Pr(XeA) can be ...

Similarly, after extending the definition of a p.d.f. of the discrete type, we replace,

for one random variable, Xi(x) by X's.), ... If f(z) is the p.c.f. of a

**continuous type**ofrandom variable X and if A is the set {z; a 3 a < b%, then P(A) = Pr(XeA) can be ...

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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