第5章习题参考答案 · 《概率论与数理统计教程（第三版）》

习题参考答案

习题5.3 答案

3, 3.78, 1.94.
略．
$\bar{y}=3\bar{x}-4, s_{y}^{2}=9s_{x}^{2}$ . 4—5. 略．
$\overline{y}_B = a\overline{x}_A + b,s_B = |a|s_A,R_B = aR_A,m_B = am_A + b.$ 7.略． $8.0,\frac{1}{3n}.$ 9—12.略． 13.14.
1. 1. $N\left(\theta, \frac{\theta^2}{40}\right)$ . 16. $N\left(\frac{5}{2}, \frac{1}{12}\right)$ . 17. $N\left(p, \frac{p(1 - p)}{20}\right)$ . 18. 1.06.
12.86. 20. 163, 9.23, 0.198, -0.742. 21. 0.047.

P (x _ {(n)} = k) = (1 - q ^ {k}) ^ {n} - (1 - q ^ {k - 1}) ^ {n}, P (x _ {(1)} = k) = q ^ {n (k - 1)} (1 - q ^ {n})

(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.

(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．

1. 1. 1. 1. 0.7718. 4. 0.8983. 5. 0.6854. 6. $c = u_{(1 + \alpha) / 2} / \sqrt{n}$ . 7. 略．
$Be\left(\frac{n}{2}, \frac{m}{2}\right)$ . 9. $F(1,1)$ . 10. 0.993 8. 11. 略． 12. $\sqrt{\frac{n}{n+1}}, n-1$ . 13. 0.079 8.
$F(10,5)$ . 15. -0.423 4. 16. $2(n - 1)\sigma^2$ . 17. $0(k > 1), \frac{k}{k - 2}(k > 2)$ .
$\frac{m}{m - 2} (m > 2)$ ， $\frac{2m^2(k + m - 2)}{k(m - 2)^2(m - 4)} (m > 4)$ . 19.略．20.27.21—22.略．

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. $\sum_{i=1}^{n} |x_i|$ .

(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) $\sum_{i=1}^{n} x_i^2$ .
(1) $\sum_{i=1}^{n} (x_i - \mu)^2$ ; (2) $\overline{x}$ . 11. $(x_{(1)}, x_{(n)})$ . 12. $(x_{(1)}, x_{(n)})$ .
$\left(\prod_{i=1}^{n} x_i, \sum_{i=1}^{n} x_i\right)$ . 14. $\left(\prod_{i=1}^{n} x_i, \prod_{i=1}^{n} (1 - x_i)\right)$ . 15. 略．
$\left(\overline{x},\overline{y},\sum_{i = 1}^{n}x_{i}^{2},\sum_{i = 1}^{m}y_{i}^{2}\right)$ . 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．