Question

----JAVA IMPLEMENTATION URGENTLY NEEDED ------

//Ques 3

/**

* Computes the standard Rayleigh distribution probability density function (The mathematical function describing the standard Rayleigh distribution is given by: y = [ x / (σ)^2 ] * e ^ [ (-x^2) / (2σ^2) ] where σ =sigma is the scale variable of Rayleigh distribution. The function y is called the probability density function of the standard Rayleigh distribution. Complete the method rayleigh(double x, int sigma) that returns the value of y given by the formula above

* the lab document for the actual formula) with scale parameter.

*

* @param x

* a value

* @param sigma

* scale parameter

* @return the standard Rayleigh distribution probability density function

* evaluated at x

*/

public static double rayleigh(double x, int sigma) {

return 0;

}

//Ques 6

/**

* Returns true if year is a leap year and false otherwise.

*

*

* A year is always a leap year if it is evenly divisible by 400; for all other

* years, a year is a leap year if it is evenly divisible by 4 and not evenly

* divisible by 100. For example:

*

*

* isLeapYear(2000) returns true (2000 is divisible by 400)

* isLeapYear(1900) returns false (1900 is divisible by 4 and 100)

* isLeapYear(2004) returns true (2004 is divisible by 4 but not 100)

* isLeapYear(2005) returns false (2005 is not divisible by 4)

*

*

* @param year

* a year

* @return true if year is a leap year and false otherwise

* @throws IllegalArgumentException

* if year is less than 1582 (the year the Gregorian

* calendar was adopted)

*/

public static boolean isLeapYear(int year) {

return false;

}

//Ques 9

/**

* Returns a string representation of a <code>Range</code> that is different

* than the one returned by <code>Range.toString</code>.

*

* <p>

* The returned string has the form <code>"minimum: x, maximum: y"</code> where

* x is the minimum value of the range and y is the maximum value of the range.

*

* @param r

* a Range instance

* @return a string representation of the range

*/

public static String toString(Range r) {

return false;

}

//Ques 14

/**

* Returns a new list of characters formed by shuffling the

* characters of the given list. It is a precondition that

* the given list t contains at least two elements, and that

* the number of elements is an even number. The list is not

* modified by this method.

*

* <p>

* To shuffle the characters in t, imagine splitting the list

* t in half so that the first (n / 2) characters of t are in

* one sublist, and the remaining (n / 2) characters of t are

* in the second sublist. The new returned list is formed by

* adding the first character of the first sublist to the

* new list, then adding the first character of the second sublist,

* then adding the second character of the first sublist, then

* adding the second character of the second sublist, and so on,

* until all of the characters in the two sublists are added

* to the new list.

*

* <p>

* For example, if t was the list:

*

* <pre>

* ['a', 'b', 'c', 'd', 'e', 'f']

* </pre>

*

* <p>

* then splitting t into two sublists yields:

*

* <pre>

* ['a', 'b', 'c'] and ['d', 'e', 'f']

* </pre>

*

* <p>

* Take the first two characters of each sublist and add them to the

* new list:

*

* <pre>

* ['a', 'd']

* </pre>

*

* <p>

* Then take the next two characters of each sublist and add them to the

* new list:

*

* <pre>

* ['a', 'd', 'b', 'e']

* </pre>

*

* <p>

* Then take the next two characters of each sublist and add them to the

* new list:

*

* <pre>

* ['a', 'd', 'b', 'e', 'c', 'f']

* </pre>

*

* @param t a non-null list of characters

* @return a new list equal to the shuffle of the characters in t

* @pre. t is not null

* @pre. t.size() is greater than or equal to 2

* @pre. t.size() is an even number

*/

public static List<Character> shuffle(List<Character> t) {

}

Answer 1

/**
* Computes the standard Rayleigh distribution probability density function (The mathematical function describing the standard Rayleigh distribution is given by: y = [ x / (σ)^2 ] * e ^ [ (-x^2) / (2σ^2) ] where σ =sigma is the scale variable of Rayleigh distribution. The function y is called the probability density function of the standard Rayleigh distribution. Complete the method rayleigh(double x, int sigma) that returns the value of y given by the formula above

* the lab document for the actual formula) with scale parameter.

*

* @param x

* a value

* @param sigma

* scale parameter

* @return the standard Rayleigh distribution probability density function

* evaluated at x

*/


public static double rayleigh(double x, int sigma) {
    double power = (-1 * Math.pow(x, 2) / (2.0 * Math.pow(sigma, 2)));
    double first = x/Math.pow(sigma, 2);

    return first * Math.pow(Math.E, power);

}

//Ques 6

/**

* Returns true if year is a leap year and false otherwise.

*

*

* A year is always a leap year if it is evenly divisible by 400; for all other

* years, a year is a leap year if it is evenly divisible by 4 and not evenly

* divisible by 100. For example:

*

*



* isLeapYear(2000) returns true (2000 is divisible by 400)

* isLeapYear(1900) returns false (1900 is divisible by 4 and 100)

* isLeapYear(2004) returns true (2004 is divisible by 4 but not 100)

* isLeapYear(2005) returns false (2005 is not divisible by 4)

*

*

* @param year

* a year

* @return true if year is a leap year and false otherwise

* @throws IllegalArgumentException

* if year is less than 1582 (the year the Gregorian

* calendar was adopted)

*/

public static boolean isLeapYear(int year) {
        return ((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0);
}

//Ques 9

/**

* Returns a string representation of a <code>Range</code> that is different

* than the one returned by <code>Range.toString</code>.

*

* <p>

* The returned string has the form <code>"minimum: x, maximum: y"</code> where

* x is the minimum value of the range and y is the maximum value of the range.

*

* @param r

* a Range instance

* @return a string representation of the range

*/

public static String toString(Range r) {
    return "(" + r.getMinimum() + ", " + r.getMaximum() + ")";

}

//Ques 14

/**

* Returns a new list of characters formed by shuffling the

* characters of the given list. It is a precondition that

* the given list t contains at least two elements, and that

* the number of elements is an even number. The list is not

* modified by this method.

*

* <p>

* To shuffle the characters in t, imagine splitting the list

* t in half so that the first (n / 2) characters of t are in

* one sublist, and the remaining (n / 2) characters of t are

* in the second sublist. The new returned list is formed by

* adding the first character of the first sublist to the

* new list, then adding the first character of the second sublist,

* then adding the second character of the first sublist, then

* adding the second character of the second sublist, and so on,

* until all of the characters in the two sublists are added

* to the new list.

*

* <p>

* For example, if t was the list:

*

* <pre>

* ['a', 'b', 'c', 'd', 'e', 'f']

* </pre>

*

* <p>

* then splitting t into two sublists yields:

*

* <pre>

* ['a', 'b', 'c'] and ['d', 'e', 'f']

* </pre>

*

* <p>

* Take the first two characters of each sublist and add them to the

* new list:

*

* <pre>

* ['a', 'd']

* </pre>

*

* <p>

* Then take the next two characters of each sublist and add them to the

* new list:

*

* <pre>

* ['a', 'd', 'b', 'e']

* </pre>

*

* <p>

* Then take the next two characters of each sublist and add them to the

* new list:

*

* <pre>

* ['a', 'd', 'b', 'e', 'c', 'f']

* </pre>

*

* @param t a non-null list of characters

* @return a new list equal to the shuffle of the characters in t

* @pre. t is not null

* @pre. t.size() is greater than or equal to 2

* @pre. t.size() is an even number

*/
public static List<Character> shuffle(List<Character> t) {
    List<Character> r= new ArrayList<>();

    int l = t.size();
    for(int i=0; i<l/2; i++) {
        r.add(t.get(i));
        r.add(t.get(i + l/2));
    }

    return r;
}