###### An Introduction to Probability and Statistical Inference

142 SOLVED PROBLEMS

Question: 11.APP.5

## The Normal Case (continued) Testing Further Hypotheses About the Mean In reference to ...

Here n\theta_{1}=2{5},\,n\theta_{2}=7{5},[/...
Question: 11.APP.4

## The Normal Case (continued) Testing Hypotheses About the Variance Refer to Example 12 , ...

Here \chi_{n;1-\alpha}^{2}~=~\chi_{40;0.975...
Question: 11.APP.3

## The Normal Case: Testing Hypotheses About the Mean Refer to Example 11 and observe that ...

Here $z_{\alpha}=z_{0.01}=2.33,$ so t...
Question: 2.26

## Let P(C)P(C^c) > 0. Then the inequalities P(A | C) > P(B | C) and P(A | C^c) > P(B | C^c) ...

The inequalities P(A\mid C)\gt P(B\mid C)[/...
Question: 2.31

## Out of a set of 3 keys, only 1 opens a certain door. Someone tries the keys successively ...

(i) ~~~P(A_{1})={\textstyle{\frac{1}{3}}};\...
Question: 3.12

## A bus is supposed to arrive at a given bus stop at 10:00 a.m., but the actual time of ...

The p.d.f. of X is$~f(x)=1/16$ for x ...
Question: 15.8

## Construct the kernel estimate of f (x), for each x ∈ ℜ, by using the U(−1, 1) kernel; ...

Here, it is convenient to use the indicator notati...
Question: 15.7

## Refer to Example 25 in Chapter 1 (see also Example 4 here), and test the null hypothesis ...

Here m=n=15,\,{\ z_{0.05}}=1.645,\,{\mathrm...
Question: 15.6

## Refer to Example 5 and test the hypothesis H0: F = G against the alternatives HA”:F≠G ...

In Example 5 we saw that R_{X}=26\ (\mathrm...
From Table 15.2,we have: Z_{1}=0,~~Z_{2}=1,...