An Introduction to Probability and Statistical Inference 1st. Edition by George G. Roussas | 9780080495750 | 0080495753

Statistical Mechanics

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 ...

Verified Answer:

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 , ...

Verified Answer:

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 ...

Verified Answer:

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) ...

Verified Answer:

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 ...

Verified Answer:

(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 ...

Verified Answer:

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; ...

Verified Answer:

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 ...

Verified Answer:

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 ...

Verified Answer:

In Example 5 we saw that

R_{X}=26\ (\mathrm...

Question: 15.4

Refer to Example 25 in Chapter 1 regarding the plant height (in 1/8 inches) of ...

Verified Answer:

From Table 15.2,we have:

Z_{1}=0,~~Z_{2}=1,...