Stat 2000: Tips for Assignment 3

Published: Thu, 11/01/12


 
My tips for Assignment 3 are coming below, but first a couple of announcements.
 
Please note that my final exam prep seminar for Stat 2000 will be on Sunday, Dec. 2, in room 100 St. Paul's College, from 9 am to 9 pm .  For complete info about the seminar, and to register if you have not done so already, click this link:
Stat 2000 Seminar 
 
I am also offering seminars in Calculus, Linear Algebra, and Stat 1000 in the coming weeks.  You can get info about those seminars here:
Grant's One-Day Exam Prep Seminars
 
If you ever want to look back over a previous tip I have sent, do note that all my tips can be found in my archive.  Click this link to go straight to my archive: 
Grant's Homework Help Archive
 
Make sure you have read my Tips on How to Do Well in this Course
 
Did you miss my Tips on what kind of calculator you should get? Click here
 
Did you miss my tips for Assignment 2? Click here
 
Tips for Assignment 3
 
You need to study Lesson 6: Discrete Probability Distributions (this also includes the Binomial and Poisson Distributions; if you are using a considerably older edition of my book, you may have those two distributions taught in a separate Lesson 7).  I am also surprised to see a lot of probability questions on this assignment that are from Stat 1000.  Make sure you look at this important set of examples and notes on probability I sent earlier:
Stat 2000: Extra Help with Probability 
 
Question 1:
If you are ever asked to decide if a particular situation is binomial or not, remember, to be binomial, four conditions must be satisfied:
(i)  There must be a fixed number of trials, n.
(ii)  Each trial must be independent.
(iii)  Each trial can have only two possible outcomes, success or failure, and the probability of success on each trial must have a constant value, p.
(iv) X, the number of successes, is a discrete random variable where
X = 0, 1, 2, ... n.
Hints for question 1: If you are reading off numbers from a randomly selected row in the random number table, note that every row has 40 digits.  That is like 40 trials looking for whatever digit you may be looking for.  What is the probability that, at any moment on the table, the next digit is a 0, or a 1, or a 2, etc.?
 
If you are selecting objects, are you sampling with replacement (independent trials) or without replacement (dependent trials)?
 
Question 2 is very similar to my question 18 in the Extra Help with Probability handout I have given you. I certainly recommend you make a three-circle Venn Diagram to solve this problem.
 
Question 2 (h) and (j) are examples of conditional probability.  I also discuss conditional probability in the handout, above.
 
Do you notice what kind of method you need to use to solve question 2 (k) and (l)?
 
Question 3 is a two-way table problem similar to my question 13 in the handout above.  You will also want to take a look at my questions 3 and 4 in that handout for an example of writing out the distribution of X.  Go through each outcome in your sample space and determine the value of X first.  For example, one of the outcomes in the sample space you listed in part (a) would be "13" meaning you selected a 1 first, then a 3 second (you might write it as 1:3 or 1;3 or something so that it is not mistaken for thirteen).  Then X=1 since of the two numbers 1 and 3,1 is the minimum.  On the other hand, for the outcome"42", X=2 since that is the minimum between 4 and 2; for "33" X=3 since both numbers are a 3.
 
Note that question 3(e) is a conditional probability.
Questions 3(f) and (g) are using the formulas for mean and variance I show you at the start of Lesson 6 (questions 1, 2 and 3).
 
Question 4 is very challenging.  You have two normal distributions, X1 and X2.  You can use the properties of mean and variance I teach in Lesson 4 to work out the mean and variance of X1 + X2.  Since X1 and X2 are both normal distributions, X1 + X2 is also normal.  Part (b) wants X1 < X2 which can also be written X1 - X2 < 0.  Again, you can find the mean and variance of X1 - X2. Of course, to change your score into a z-score, you will have to use the standardizing formula you first learned in Stat 1000, z = (x - mu)/sigma or z = (x - μ)/σ.
 
Question 5 is obviously binomial.
 
Question 6 is similar to a question I teach in Lesson 6 in the "Hypothesis Testing Revisited" section.  Note that you can use Table C to solve the probabilities more quickly.
 
Questions 6 and 7 are obviously Poisson Distribution questions similar to my examples in Lesson 6.