I need help with this question Let Ui represent a random var

I need help with this question

Let U_i represent a random variable uniformly distributed on (0, 1), i.e. what the computer you when you execute \"rand().\" (a) What distribution do you get for U_1 + u_2? Can you describe it analytically? (b) What distribution do you get for max(U_1, u_2)? Can you describe it analytically? (c) What distribution do you get for min (U_1, u_2)? Can you describe it analytically? (c) What distribution do you get for max(u_1, u_2, u_3)? Can you describe it analytically?

Solution

Dear Student,

When we execute rand function it gives us a random number, rand() will return an integer from 0 to 32767 depending on implementation.The generation of random number can also be controlled.If we want to execute a random number between 1 to 10 then following program demonstrate this...

program...

#include<stdio.h>
int main()
{
    int random=rand()%10+1;
    printf(\"%d\ \",random);
    return 0;
}

Output: 4

Every time when you compile and the run the the program you will get different number.

In the above question u_{i is} in the range of (0,1)....so....

Answer No..1

for u1+u2 the following program demonstrate this...i created two random number that is stored on u1 and u2 varibale.and the sum of the number is stored on u variabel.The output that we get is the addition of two random number.

#include<stdio.h>
int main()
{
    int u1=rand()%1+1;
    int u2=rand()%1+1;
    int u=u1+u2;
    printf(\"%d\ \",u);
    return 0;
}

Output: 2

Answer No-2 Finding max of two numbers.In the below program we are finding max of two random number.

program

#include<stdio.h>
int main()
{
int u1=rand()%1;
int u2=rand()%1+1;
int u=min(u1, u2);
printf(\"%d\",u);
}
int min(int min, int max)
{

if(min>max)
   return min;

else

return max;
}

output=1

Answer-3-Finding min of two numbers.In the below program we are finding min of two random number.

#include<stdio.h>
int main()
{
int u1=rand()%1;
int u2=rand()%1+1;
int u=min(u1, u2);
printf(\"%d\",u);
}
int min(int min, int max)
{

if(min<max)
   return min;

else

return max;
}

Answer-4-for max(v1,v2,v3)

program==

#include<stdio.h>
int main()
{
int u1=rand()%1;
int u2=rand()%1;
int u3=rand()%1+1;
int u=max(u1, u2, u3);
printf(\"%d\",u);
}
int max(int a, int b, int c)
{
    if(a>b && a>c)
   return a;
   else if(b>a && b>c)
   return b;
   else
   return c;
}

output=1

all the example are tested in the range of (0,1) as assume in the question paper.