Write a java Binomial class to implement a Binomial random variable. Private instance variables for the class should include:

double P - probability of a success in any one trial.

long N - number of independent trials.

long X - the number of successes in the N trials.

The class methods should include:

appropriate constructor(s).

appropriate get and set methods for the instance variables.

long randomX() - generates a new random value for X.

double mean() - calculates the mean of the random variable [= N*P].

double variance() - calculates the variance of random variable [= N*P*(1-P)].

double probX() - calculates the Binomial probability for the current X value.

Write a program that uses the Binomial class to solve the following problems:

1. For the Binomial distribution defined by P = 0.36 and N = 22:

a. Output P and N.

b. Generate a random value for X, and then output that value.

c. Output the mean of the distribution.

d. Output the variance of the distribution

2. For the Binomial distribution defined by P = 0.73 and N = 6, output the probability distribution of X. That is, for each value of X from 0 to 6, show the X-value together with the probability for that value. Output format should be:

X Pr(X)

0 ...

1 ...

... ...

6 ...

3. For the Binomial distribution defined by P = 0.32 and N = 12:

a. Generate 100 random variable values.

b. Calculate the average of these generated values [= (X₁ + X₂ + ... + X₁₀₀)/100].

c. Calculate the theoretical mean of this probability distribution using the mean() method.

d. Compare the values obtained in 3b and 3c. How close are they? Why aren't the values identical?