## Introduction to Mathematical Statistics |

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Page 54

Let the outcome of these n repetitions be denoted respectively by the random

variables X1, X2, ..., Xn. Then we call X1, X2,..., Xn the items of a

from the distribution under consideration. Comments. Let it be assumed that the ...

Let the outcome of these n repetitions be denoted respectively by the random

variables X1, X2, ..., Xn. Then we call X1, X2,..., Xn the items of a

**random sample**from the distribution under consideration. Comments. Let it be assumed that the ...

Page 55

In the first of these examples the p.a.f. of the random variable Y = X1 + X2 was

obtained; here Y is the sum of the two items of the

we found the p.a.f. of the sum Y = XH + X2 + ... + Xn of the n items of the random ...

In the first of these examples the p.a.f. of the random variable Y = X1 + X2 was

obtained; here Y is the sum of the two items of the

**random sample**. In Example 4we found the p.a.f. of the sum Y = XH + X2 + ... + Xn of the n items of the random ...

Page 57

Find the probability that exactly four items of a

distribution having p.d.f. f(z) = (x + 1)/2, — 1 < z < 1, zero elsewhere, exceed zero.

• 3.26. Let X1, X2, Xs be a

Find the probability that exactly four items of a

**random sample**of size 5 from thedistribution having p.d.f. f(z) = (x + 1)/2, — 1 < z < 1, zero elsewhere, exceed zero.

• 3.26. Let X1, X2, Xs be a

**random sample**of size 3 from a normal distribution ...### 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