## Introduction to Mathematical Statistics |

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Page 11

Compute P(A) = Pr[XeA1], P(A2) = Pr[XeA2], and PIA1 \J A2] - Pr[XeA1\J A2]. v1.

13. Let the

s a < 1}, find P(A2) if P(A) = %. 1.14. Let the

and ...

Compute P(A) = Pr[XeA1], P(A2) = Pr[XeA2], and PIA1 \J A2] - Pr[XeA1\J A2]. v1.

13. Let the

**sample space**A = {2; 0 < r < 1}. If A1 = {z; 0 < r < 3%; and A2 = {z; %s a < 1}, find P(A2) if P(A) = %. 1.14. Let the

**sample space**be A = {z; 0 < r < 10}and ...

Page 12

1 \4 f(x) =#: #() , re-A, and, as usual, 0! = 1. Then if A = {z; a = 0, 1}, we have 4! (1

\* . 4.1 / 1 \* 5 Pr(XeA) -:() ++() = 16 EXAMPLE 2. Let the

1, 2, 3, ...}, and let 1 a: f(z) = () , re.A. If X is a random variable of the discrete type

...

1 \4 f(x) =#: #() , re-A, and, as usual, 0! = 1. Then if A = {z; a = 0, 1}, we have 4! (1

\* . 4.1 / 1 \* 5 Pr(XeA) -:() ++() = 16 EXAMPLE 2. Let the

**sample space**A = {z; z =1, 2, 3, ...}, and let 1 a: f(z) = () , re.A. If X is a random variable of the discrete type

...

Page 166

We shall compare two such tests, and to keep the exposition simple, the size of

the random

the

...

We shall compare two such tests, and to keep the exposition simple, the size of

the random

**sample**will be taken to be n = 2. With a random**sample**of size n = 2,the

**space**A of positive probability density consists of a part of the first quadrant of...

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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