2658 - 概率论与数理统计练习题

1、将一枚均匀的硬币连掷三次，其中有两次都出现正面的概率为

A.0.125 B. 0.25 C. 0.375 D. 0.5

2、设随机变量X的概率密度为，则c值为

<span>A.</span>－<span>0.5&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;B. 0&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;C. 0.5&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;D. 1</span>

<span>3</span>、设随机变量<img src="http://tk.hustoj.com:80/attached/image/20140511/20140511104042_84548.png" alt="" />，则<span>E[X<sup>2</sup>]</span> 值为<span></span>

<span>A. 0.25&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B. 0.5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C. 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D. 1.25</span>

<span>4</span>、设X的分布函数为F(x)，则Y=3X+1的分布函数G(y)为<span></span>

<span>A. F(y/3-1/3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B. F(3y+1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C. 3F(y)+1&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;D. F(y)/3-1/3</span>

<span>5</span>、如果X,Y,满足D(X+Y)=D（X-Y），则必有<span></span>

<span>A. X</span>与<span>Y</span>独立&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span>B. X</span>与<span>Y</span>不相关<span>&nbsp;&nbsp;&nbsp;&nbsp; </span><span>C. D(X)=0&nbsp; </span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span>&nbsp;D. D(Y)=0</span>

<br />

6、设随机变量<span>X</span>服从（–<span>a</span>，<span>2a</span>）上的均匀分布，<span>E[X]=3</span>，则<span>a</span>值为<span></span>

<span>A. 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B. 3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C. 6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D. 12</span>

7、设标准正态分布的上<span>0.05</span>分位点为<i><span>z</span></i>=1.645,则分布函数在该点的函数值为<span></span>

<span>A. 0.05&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B. 1.645&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;C. 0.95&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D. 1</span>

8、设总体期望为<span>0</span>.<span>50</span>，方差为<span>0</span>.<span>0001</span>，容量为<span>16</span>的样本均值为<span>0</span>.<span>54</span>，则<span>U</span>统计量的值为<span></span>

<span>A. 0.0001&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B. 0.50&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C. 0.54&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D. 16</span>

9、已知事件A，B相互独立且互不相容，P(AB)=<u> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</u><u></u>

<u><br />

10、<span style="line-height:1.5;">甲、乙两人独立的对同一目标射击一次，其命中率分别为0.6和0.5，现已知目标被命中，则它是甲射中的概率为（三位小数）</span><u>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</u><span style="line-height:1.5;">。</span>

<span></span>

<br />

<span style="line-height:1.5;"><br />

<span style="line-height:1.5;">11、</span><span style="line-height:1.5;">设</span><span style="line-height:1.5;"></span><span style="line-height:1.5;">是来自正态总体</span><span style="line-height:1.5;"><img src="http://tk.hustoj.com:80/attached/image/20140511/20140511122127_31218.png" alt="" /></span><span style="line-height:1.5;">的样本，令</span><span style="line-height:1.5;"><img src="http://tk.hustoj.com:80/attached/image/20140511/20140511122137_96077.png" alt="" /></span><span style="line-height:1.5;"><br />

则当C= 时，CY～。

<span style="line-height:1.5;"><br />

<span style="line-height:1.5;">12、设<span>X</span>、<span>Y</span>相互独立，<span>E[X]=</span><i>a</i>，<span>E[Y] =</span><i>b</i>，E[X<sup>2</sup>]=<i>c</i>，<span>E[Y<sup>2</sup>]=d</span>，则<span>E[</span><i>b</i>X–<i>a</i>Y]为多少？</span>

<span style="line-height:1.5;"><br />

<span style="line-height:1.5;">13、设总体<span>X</span>服从<span>(0, </span><i>a</i>)上的均匀分布，其中<i>a</i>未知。今对<span>X</span>进行<span>10</span>次简单抽样，样本<span></span>的观测值为<span>0.60</span>、<span>0.58</span>、<span>0.61</span>、<span>0.55</span>、<span>0.59</span>、<span>0.63</span>、<span>0.52</span>、<span>0.67</span>、<span>0.49</span>、<span>0.62</span>。试用矩估计法由一阶矩估计<i>a</i>的值<span>（三位小数）</span>。</span>

<span style="line-height:1.5;"><br />

<span style="line-height:1.5;">14、<span>设总体</span><span>X</span><span>服从</span><span>(0,&nbsp;</span><i>a</i><span>)上的均匀分布，其中</span><i>a</i><span>未知。今对</span><span>X</span><span>进行</span><span>10</span><span>次简单抽样，样本</span><span></span><span>的观测值为</span><span>0.60</span><span>、</span><span>0.58</span><span>、</span><span>0.61</span><span>、</span><span>0.55</span><span>、</span><span>0.59</span><span>、</span><span>0.63</span><span>、</span><span>0.52</span><span>、</span><span>0.67</span><span>、</span><span>0.49</span><span>、</span><span>0.62</span><span>。试用矩估计法由二阶矩估计</span><i>a</i><span>的值<span>（三位小数）</span>。</span><span></span></span>

<span style="line-height:1.5;"><br />

<span style="line-height:1.5;">15、设一机电系统由四种零件构成，它们分别占系统的<span>94%</span>、<span>3%</span>、<span>2%</span>、<span>1%</span>，四种零件的故障率依次为<span>0.02</span>，<span>0.05</span>，<span>0.10</span>，<span>0.15</span>。若任意零件出故障，则整个系统不能正常工作。求该机电系统能正常工作的概率<span>（三位小数）</span>？</span>

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C语言解答

#include "stdio.h"
 
int main()
{
    int a;
    float b;
    char c;
    while(scanf("%d",&a) != EOF)
 {
  switch(a){
  	case 0: printf("1\n");break;
  	case 1: c='C';break;
  	case 2: c='C';break;
  	case 3: c='D';break;
  	case 4: c='A';break;
  	case 5: c='B';break;
  	case 6: c='C';break;
  	case 7: c='C';break;
  	case 8: c='D';break;
  	case 9:  printf("0\n");break;
  	case 10: b=0.75;break;
  	case 11: printf("8\n");break;
  	case 12: printf("0\n");break;
  	case 13: b=0.586*2;break;
  	case 14: b=1.018;break;
  	case 15: b=0.976;//b=0.94*0.02+0.03*0.05+0.02*0.10+0.01*0.15;break;
  	
  }
   if(a==1||a==2||a==3||a==4||a==4||a==5|a==6||a==7||a==8)
   printf("%c\n",c);
   else if(a==10||a==13||a==14||a==15)
   printf("%.3f\n",b);
  }
    return 0;
}

C++解答

#include <stdio.h>
 int main()
 {
    int a;
    while(scanf("%d",&a) != EOF)
 {
      if (a==1)
      { 
        printf("C\n");
	  }
      else if (a==2)
	  {
        printf("C\n");
	  }
     else if (a==3)
	 {
		 printf("D\n");
	 }
    else if (a==4)
	{
        printf("A\n");
	}
    else if (a==5)
	{
        printf("B\n");
	}
    else if (a==6)
	{
        printf("C\n");
	}
    else if (a==7)
	{
        printf("C\n");
	}
    else if (a==8)
	{
        printf("D\n");
	}
    else if (a==9)
	{
        printf("0\n");
	}
    else if (a==10)
	{
        printf("0.750\n");
	}
    else if (a==11)
	{
        printf("8\n");
	}
    else if (a==12)
	{
        printf("0\n");
	}
    else if (a==13)
	{
        printf("1.172\n");
	}
    else if (a==14)
	{
        printf("1.019\n");
	}
    else if (a==15)
	{
        printf("0.976\n");
	 }
	else 
	 {
		printf("1");
	}
}
    return 0;
 }

时间限制	1 秒
内存限制	128 MB

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2658 - 概率论与数理统计 练习题

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2658 - 概率论与数理统计练习题