第5章 习题参考答案

习题参考答案

习题5.3 答案

1. 3, 3.78, 1.94.

2. 略.

3. $\bar{y}=3\bar{x}-4,s_y^2=9s_x^2$ . 4—5. 略.

4. ${\overline{y}}_B=a{\overline{x}}_A+b,s_B=|a|s_A,R_B=a{R}_A,m_B=a{m}_A+b.$ 7.略. $8.0,\frac{1}{3n}.$ 9—12.略. 13.14.

5. 68. 15. $N\left(\theta ,\frac{{\theta }^2}{40}\right)$ . 16. $N\left(\frac{5}{2},\frac{1}{12}\right)$ . 17. $N\left(p,\frac{p(1-p)}{20}\right)$ . 18. 1.06.

6. 12.86. 20. 163, 9.23, 0.198, -0.742. 21. 0.047.

$x_{(1)}$	1	2	3	4	5
P	0.590 4	0.28	0.104	0.024	0.001 6
$x_{(4)}$	1	2	3	4	5
P	0.001 6	0.024	0.104	0.28	0.590 4

$$P(x_{(n)}=k)=(1-q^k{)}^n-(1-q^{k-1}{)}^n,P(x_{(1)}=k)=q^{n(k-1)}(1-q^n)$$

24. (1) 0.937 0; (2) 0.330 8. 25. 略. 26. $p_{m_{0.5}}(x)=3780x^9(1-x{)}^9(3-2x{)}^4(2x+1{)}^4$ .

27—28. 略. 29. (1) $\frac{6}{11},\frac{5}{242}$ ; (2) 0.0014.

30. (1) $N\left(0.5,\frac{1}{9n}\right)$ ; (2) $N\left(\mu ,\frac{\pi {\sigma }^2}{2n}\right)$ ; (3) $N\left(\frac{\sqrt{2}}{2},\frac{1}{8n}\right)$ ; (4) $N\left(0,\frac{1}{n{\lambda }^2}\right)$ .

31—36. 略.

习题 5.4

1. 4. 2. 62. 3. 0.7718. 4. 0.8983. 5. 0.6854. 6. $c=u_{(1+\alpha )/2}/\sqrt{n}$ . 7. 略.

2. $Be\left(\frac{n}{2},\frac{m}{2}\right)$ . 9. $F(1,1)$ . 10. 0.993 8. 11. 略. 12. $\sqrt{\frac{n}{n+1}},n-1$ . 13. 0.079 8.

3. $F(10,5)$ . 15. -0.423 4. 16. $2(n-1){\sigma }^2$ . 17. $0(k>1),\frac{k}{k-2}(k>2)$ .

4. $\frac{m}{m-2}(m>2)$ ， $\frac{2m^2(k+m-2)}{k(m-2{)}^2(m-4)}(m>4)$ . 19.略．20.27.21—22.略.

习题 5.5

1—4. 略. 5. $\frac{1}{n}{\sum }_{i=1}^n\ln x_i$ . 6. ${\sum }_{i=1}^n{x}_i^m$ . 7. $\frac{1}{n}{\sum }_{i=1}^n\ln x_i$ . 8. ${\sum }_{i=1}^n|x_i|$ .

9. (1) $\overline{x}$ ; (2) $x_{(n)}$ ; (3) $\left({\sum }_{i=1}^n\ln x_i,{\sum }_{i=1}^n{\ln }^2{x}_i\right)$ ; (4) ${\sum }_{i=1}^n{x}_i^2$ .

10. (1) ${\sum }_{i=1}^n(x_i-\mu {)}^2$ ; (2) $\overline{x}$ . 11. $(x_{(1)},x_{(n)})$ . 12. $(x_{(1)},x_{(n)})$ .

11. $\left({\prod }_{i=1}^n{x}_i,{\sum }_{i=1}^n{x}_i\right)$ . 14. $\left({\prod }_{i=1}^n{x}_i,{\prod }_{i=1}^n(1-x_i)\right)$ . 15. 略.

12. $\left(\overline{x},\overline{y},{\sum }_{i=1}^n{x}_i^2,{\sum }_{i=1}^m{y}_i^2\right)$ . 17. $\left({\sum }_{i=1}^n{x}_i,{\sum }_{i=1}^n{x}_i^2,{\sum }_{i=1}^n{y}_i,{\sum }_{i=1}^n{y}_i^2,{\sum }_{i=1}^n{x}_i{y}_i\right)$ . 18—20.略.