Problem
1. Implement a Java class PieChart that displays a pie chart to the probabilities of the n most
frequent occurrences of an event to be specified in part II of the exercise. The probability
of event is given by the equation:
probability of event = frequency of event / total frequencies of all events
In the pie chart:
i. The area of each segment is proportional to the probability of the corresponding event:
probability of event = Central angle of segment / 2pi
ii. Each segment has a different color;
iii. Each segment has a legend showing the event and its probability;
iv. The last segment represents “All Other Events” and their cumulative probability. For
example, in the graph below where the event is the occurrence of a letter in a text: n=
3, and the probability of All Other Events is one minus the sum of the probabilities of
events e, s, and I;
<p align="center"<img src="Chart.PNG"/</p
2. The PieChart class includes appropriate constructors and a method draw that draws the
pie chart. The drawing panel should use a layout manger and include appropriate GUI
components to input the number of events, n and display the pie chart together with the
vents probabilities. You may amend and use the class hierarchy in previous exercise, but
in any case, you may only use your own classes and methods for the operations include.
3. Implement a Java class HistogramLetters that calculates the n most frequent letters in the
file “Emma.txt” and their probabilities. The HistogramLetters class utilizes the drawing
panel in Part I to draw a pie chart to the letter probabilities.
