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Juliette [100K]
2 years ago
11

A detective agency is looking to bust an arms sale. According to available intelligence, the sale is likely to happen in one of

the three locations A, B, or C. Historical patterns indicate that P(A) (the likelihood that the sale will happen at A) is twice that of P(B), and likewise, P(B) = 2P(C). What is the probability distribution of the arms sale happening in these 3 places? Let us denote the location of the sale with a memoryless source X, i.e., X takes values ‘A’, ’B’, ’C’, with probabilities P(A), P(B), and P(C) respectively. Calculate it’s entropy H(X) in bits. Note that H(X) represents the amount of uncertainty in the location of the sale. The director of the agency is not very happy with the level of uncertainty. So he looks up recent covert transmissions for hints. He finds a recent coded message from agent Atomic Blonde which indicates that the sale will not happen at C. Let us denote the message from agent Blonde as Y , and in this case Y ="not C". Given this information, what is the new uncertainty H(X|Y = "not C")?
Computers and Technology
1 answer:
Paha777 [63]2 years ago
4 0

Answer:

Probability Distribution={(A, 4/7), (B, 2/7), (C, 1/7)}

H(X)=5.4224 bits per symb

H(X|Y="not C")=0.54902 bits per symb

Explanation:

P(B)=2P(C)

P(A)=2P(B)

But

P(A)+P(B)+P(C)=1

4P(C)+2P(C)+P(C)=1

P(C)=1/7

Then

P(A)=4/7

P(B)=2/7

Probability Distribution={(A, 4/7), (B, 2/7), (C, 1/7)}

iii

If X={A,B,C}

and P(Xi)={4/7,2/7,1/7}

where  Id =logarithm to base  2

Entropy, H(X)=-{P(A) Id P(A) +P(B) Id P(B) + P(C) Id P(C)}

=-{(1/7)Id1/7 +(2/7)Id(2/7) +(4/7)Id(4/7)}

=5.4224 bits  per symb

if P(C)  =0

P(A)=2P(B)

P(B)=1/3

P(A)=2/3

H(X|Y="not C")= -(1/3)Id(I/3) -(2/3)Id(2/3)

=0.54902 bits per symb

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Answer:

Here is the C++ program:

#include <iostream>  //to use input output functions

using namespace std;   //to identify objects like cin cout

int main(){  //start of main function

       int MinFloors = 1;  //minimum number of floors

       int MinRooms  = 10; //minimum number of rooms

       int NoOfFloors;  //stores number of floors

       int NoOfRooms;  //stores number of rooms

       int OccupiedRooms;  //stores number of rooms occupied

       double TotalRooms=0, TotalOccupied=0;   //stores computed total number of rooms and total number of occupied rooms

       cout<<"How many floors does the hotel have? ";  //prompts user to enter number of floors

       do{  //iterates until the user enters valid number of floors

           cout<<"(cannot be less than "<<MinFloors<<"): ";  //error message

           cin >>NoOfFloors;  //reads number of floors from user

       }while(NoOfFloors<MinFloors);  //repeats as long as number of floors is less than minimum number of floors

       for(int floor=1; floor <= NoOfFloors; floor++){    //iterates through the floors to skip third iteration

           if(floor == 3){   //if floor is third floor

               continue;             }  

           cout<<"How many rooms are on floor " <<floor;  //prompts user to enter number of floors

           do{  //start of do while loop

               cout<<"(cannot be less than "<<MinRooms<<"): ";  //error message

               cin >>NoOfRooms;  //reads number of rooms from user

           }while(NoOfRooms<MinRooms);    //iterates as long as number of rooms are less than valid minimum number of rooms

           TotalRooms += NoOfRooms;   //adds number of rooms to the count of total number of rooms

           cout<<"How many of those rooms are occupied?";  //prompts user to enter number of rooms occupied

           do{  //start of do while loop

         cout<<"(cannot be less than 0 or greater than "<<NoOfRooms<<"): ";  //generates error message

         cin >>OccupiedRooms;  //reads number of rooms occupied by user

           }while(OccupiedRooms<0 || OccupiedRooms>NoOfRooms);   //iterates as long as the number of occupied rooms are less than 0 or greater than number of rooms

           TotalOccupied += OccupiedRooms;    }    //adds number of rooms occupied to the count of total number of occupied rooms    

       cout<<"\nThe hotel has a total of "<<TotalRooms<<" rooms"<<endl;  //displays the total number of rooms in the hotel

       cout<<TotalOccupied<<" are occupied."<<endl;  //displays the total number of occupied rooms

       cout<<(TotalRooms-TotalOccupied)<<" are unoccupied."<<endl;  //displays the total number of unoccupied rooms

cout<<"The occupancy rate is: "<<100*(TotalOccupied/TotalRooms)<<"%"<<endl;     }  //computes and displays the occupancy rate

   

Explanation:

The program first prompts the user to enter number of floors in the hotel. Lets say user enters 6. This is stored in NoOfFloors So

NoOfFloors = 6

So the loop runs for 6 times

Next it asks user to enter the number of rooms in the floor 1. Lets say user enters 12 so this is stored in NoOfRooms so

NoOfRooms = 12

TotalRooms += NoOfRooms;

this statement keeps adding number of rooms to TotalRooms so

TotalRooms = 12

Next program asks user about the number of occupied rooms. Lets say user enters 10 so this is stored in OccupiedRooms so

OccupiedRooms = 10

this statement keeps adding number of rooms to TotalOccupied so

 TotalOccupied += OccupiedRooms;

TotalOccupied = 10

At next iteration program asks user again to enter number of rooms in floor 2. Suppose user enters 14 so

NoOfRooms = 12

TotalRooms += NoOfRooms;

TotalRooms = 12+14

TotalRooms = 26

Program asks again to enter number of occupied rooms so it becomes:

OccupiedRooms = 8

this statement keeps adding number of rooms to TotalOccupied so

 TotalOccupied += OccupiedRooms;

TotalOccupied = 10+8

TotalOccupied = 18

Next is skips floor 3 and iteration 3. and asks user to enter number of rooms in floor 4. Suppose user enters 14

Number of rooms become:

TotalRooms = 12+14+14

TotalRooms = 40

and suppose user enters 14 as occupied rooms so total occupied become:

TotalOccupied = 10+8 + 14

TotalOccupied = 32

For floor 5: Suppose user enters 13

TotalRooms = 12+14+14+13

TotalRooms = 53

For floor 5: Suppose user enters 10

TotalOccupied = 10+8 + 14+10

TotalOccupied = 42

For floor 6: Suppose user enters 12

TotalRooms = 12+14+14+13+12

TotalRooms = 65

For floor 6: Suppose user enters 11

TotalOccupied = 10+8 + 14+10+11

TotalOccupied = 53

Now the loop breaks

Hence

TotalRooms = 65

TotalOccupied  = 53

total unoccupied = TotalRooms-TotalOccupied = 65-53 = 12

The occupancy rate is: 100*(TotalOccupied/TotalRooms) = 100*(53/65) = 81.5385

The output of the program is attached in a screenshot.

6 0
3 years ago
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