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TE 3341 Probability, Statistics and Random Processes
Homework 3 (80 points)
Problem 1 (10 points)
Assignment Date: 2/7/2000 |{ Due Date: 2/16/2000
2.6 from the textbook
Problem 2 (10 points)
2.14 from the textbook
Problem 3 (20 points)
Suppose that a fair dice is tossed and a score (X) recorded. Find the density function of
3.a Sum of the scores.
3.b Minimum score.
3.c Maximum score.
Problem 4 (10 points) Use the Dice Experiment applet at http://www.math.uah.edu/stat/dist/index.html In the simulation of the dice experiment, select fair dice. Select the following random variables and note the shape
and location of the density function. Run the experiment 1000 times, updating every 10 runs. For each
variables, note the apparent convergence of the relative frequency function to the density function.
4.a Sum of the scores.
4.b Minimum score.
4.c Maximum score.
4.d Average score.
4.e Number of aces (1's)
Problem 5 (20 points)
Suppose that a coin with probability of heads p = 0.4 is tossed 5 times. Let X denote the number of
heads.
5.a Find the density function of X.
5.b Graph the density function and identify the mode.
5.c Find P(X > 3).
Problem 6 (10 points)
Use the Binomial Coin Experiment applet at http://www.math.uah.edu/stat/dist/index.html. In
the simulation of the coin experiment, set n = 5 and p = 0.4. Run the experiment 1000 times, updating
every 10 runs, and note the apparent convergence of the relative frequency function of X to the density
function.
NOTE: You need to turn in the printouts of java applet windows for simulation problems.
To print the Java Applet window under windows, you need to select the window with the
applet and hit Alt Print Scrn. This copies the window to the clipboard (as a bitmap).
The window can then be printed from another applications (Paint, for example).
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