A datagram network allows routers to drop packets whenever they need to. The probability of a router discarding a packetis p. Co
1 answer:
Answer:
a.) k² - 3k + 3
b.) 1/(1 - k)²
c.)
Explanation:
a.) A packet can make 1,2 or 3 hops
probability of 1 hop = k ...(1)
probability of 2 hops = k(1-k) ...(2)
probability of 3 hops = (1-k)²...(3)
Average number of probabilities = (1 x prob. of 1 hop) + (2 x prob. of 2 hops) + (3 x prob. of 3 hops)
= (1 × k) + (2 × k × (1 - k)) + (3 × (1-k)²)
= k + 2k - 2k² + 3(1 + k² - 2k)
∴mean number of hops = k² - 3k + 3
b.) from (a) above, the mean number of hops when transmitting a packet is k² - 3k + 3
if k = 0 then number of hops is 3
if k = 1 then number of hops is (1 - 3 + 3) = 1
multiple transmissions can be needed if K is between 0 and 1
The probability of successful transmissions through the entire path is (1 - k)²
for one transmission, the probility of success is (1 - k)²
for two transmissions, the probility of success is 2(1 - k)²(1 - (1-k)²)
for three transmissions, the probility of success is 3(1 - k)²(1 - (1-k)²)² and so on
∴ for transmitting a single packet, it makes:
∞ n-1
T = ∑ n(1 - k)²(1 - (1 - k)²)
n-1
= 1/(1 - k)²
c.) Mean number of required packet = ( mean number of hops when transmitting a packet × mean number of transmissions by a packet)
from (a) above, mean number of hops when transmitting a packet = k² - 3k + 3
from (b) above, mean number of transmissions by a packet = 1/(1 - k)²
substituting: mean number of required packet =
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Answer:
Explanation:
The code provided worked for the most part, it had some gramatical errors in when printing out the information as well as repeated values. I fixed and reorganized the printed information so that it is well formatted. The only thing that was missing from the code was the input validation to make sure that no negative values were passed. I added this within the getMonths() method so that it repeats the question until the user inputs a valid value. The program was tested and the output can be seen in the attached image below.
import java.io.*;
import java.util.*;
class Rainfall
{
Scanner in = new Scanner(System.in);
private int month = 12;
private double total = 0;
private double average;
private double standard_deviation;
private double largest;
private double smallest;
private double months[];
public Rainfall()
{
months = new double[12];
}
public void setMonths()
{
for(int n=1; n <= month; n++)
{
int answer = 0;
while (true) {
System.out.println("Enter the rainfall (in inches) for month #" + n + ":" );
answer = in.nextInt();
if (answer > 0) {
months[n-1] = answer;
break;
}
}
}
}
public void getTotal()
{
total = 0;
for(int i = 0; i < 12; i++)
{
total = total + months[i];
}
System.out.println("The total rainfall for the year is " + total);
}
public void getAverage()
{
average = total/12;
System.out.println("The average monthly rainfall is " + average);
}
public void getLargest()
{
double largest = 0;
int largeind = 0;
for(int i = 0; i < 12; i++)
{
if (months[i] > largest)
{
largest = months[i];
largeind = i;
}
}
System.out.println("The largest amount of rainfall was " + largest +
" inches in month " + (largeind + 1));
}
public void getSmallest()
{
double smallest = Double.MAX_VALUE;
int smallind = 0;
for(int n = 0; n < month; n++)
{
if (months[n] < smallest)
{
smallest = months[n];
smallind = n;
}
}
System.out.println("The smallest amount of rainfall was " + smallest +
" inches in month " + (smallind + 1));
}
public static void main(String[] args)
{
Rainfall r = new Rainfall();
r.setMonths();
r.getTotal();
r.getSmallest();
r.getLargest();
r.getAverage();
}
}
