ECE 558 - Spring 2021

Power System Reliability

Project 2 - Due 11 Feb 2021

1. Three boxes containing Red, White, and Blue balls are used in an experiment. Box 1 contains 3R, 3W, 2B. Box 2 contains 1R, 1W, 1B. Box 3 contains 3R, 1W, 5B. The experiment consists of drawing one ball at random from Box 1 and placing it in Box 2, then drawing one ball at random from Box 2 and placing it in Box 3.
   1. Draw the cumulative distribution functions for the number of red, white, and blue balls in Box 3. Note: You need to draw three separate cdf's, one for each color.
   2. What are the expected number of red, white, and blue balls in Box 3?
   3. What are the variances of the probabilities of the number of red, white, and blue balls in Box 3?
   4. Given that at the end of the experiment, there were six blue balls in Box 3, what is the probability that a white ball was drawn from Box 1?
2. A player tosses two fair coins. He wins $1.00 if one head appears and $2.00 if two heads appear. On the other hand, he loses $5.00 if no heads appear. What is his expected gain in this game? Should he be playing this game?
3. A foreman of a casting section in a factory finds that on average 1 in every 5 castings made is defective. If the section makes 8 castings a day what is the probability that exactly 2 castings will be defective?
4. What is the probability of getting a total of 8
   1. exactly three times in four tosses of a pair of dice?
   2. at least twice in four tosses of a pair of dice?
   3. Draw the cumulative distribution function for the number of times a total of 8 is obtained in four tosses of a pair of dice.
5. A telephone exchange contains 10 lines. A line can be busy or available for calls and all lines act independently. Suppose the probability that a line will be busy during the noon period is 0.8.
   1. What is the probability of there being at least three free lines at any given time during the noon period?
   2. What is the expected number of free lines during this period?

Main Campus students must submit their assignments on paper at the beginning of the lecture. In addition, both Internet students and Main Campus students must submit an electronic copy via SafeAssignment on the ECE 558 Blackboard site BEFORE the beginning of class. SafeAssign does not allow multiple files, so you'll need to find a way to submit a single file, e.g., scanned images (PNG or JPEG) can be inserted in a Word Document. See the "Blackboard SafeAssign" link on the course home page for details. Please make sure your file is less than 1 MB in size!