# SOCR CommunityPortal Events May2007

(Difference between revisions)
 Revision as of 20:13, 18 May 2007 (view source)IvoDinov (Talk | contribs)← Older edit Revision as of 20:14, 18 May 2007 (view source)IvoDinov (Talk | contribs) Newer edit → Line 5: Line 5: * [[CP_May2007_Name_Context_Date | This is just an Example Wiki Page]] (the title of this Wiki page is [[CP_May2007_Name_Context_Date]] - use the same syntax to create your own page) * [[CP_May2007_Name_Context_Date | This is just an Example Wiki Page]] (the title of this Wiki page is [[CP_May2007_Name_Context_Date]] - use the same syntax to create your own page) - - - - - - == This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions.== - - * '''Description''':  You can access the applets for the above distributions at  http://www.socr.ucla.edu/htmls/SOCR_Distributions.html . - - * '''Exercise 1:''' Use SOCR to graph and print the following distributions and answer the questions below.  Also, comment on the shape of each one of these distributions: - **a. $X \sim b(10,0.5)$, find $P(X=3)$, $E(X)$, $sd(X)$, and verify them with the formulas discussed in class. - **b. $X \sim b(10,0.1)$,  find $P(1 \le X \le 3)$. - **c. $X \sim b(10,0.9)$, find $P(5 < X < 8), \ P(X < 8), \ P(X \le 7), \ P(X \ge 9)$. - **d. $X \sim b(30,0.1)$, find $P(X > 2)$. - - Below you can see a snapshot of the distribution of $X \sim b(20,0.3)$ - - -
[[Image: SOCR_Activities_Binomial_Christou__binomial.jpg|600px]]
- - - * '''Exercise 2:''' Use SOCR to graph and print the distribution of a geometric random variable with $p=0.2, p=0.7$.  What is the shape of these distributions?  What happens when $p$ is large?  What happens when $p$ is small? - - Below you can see a snapshot of the distribution of $X \sim geometric(0.4)$ - - -
[[Image: SOCR_Activities_Christou_geometric.jpg|600px]]
- - $\sqrt(n)$ - - * '''Exercise 3:''' Select the geometric probability distribution with $p=0.2$.  Use SOCR to compute the following: - **a. $P(X=5)$ - **b. $P(X > 3)$ - **c. $P(X \le 5)$ - **d. $P(X > 6)$ - **e. $P(X \ge 8)$ - **f. $P(4 \le X \le 9)$ - **g. $P(4 < X < 9)$ - - * '''Exercise 4:''' Verify that your answers in exercise 3 agree with the formulas discussed in class, for example, $P(X=x)=(1-p)^{x-1}p$, $P(X > k)=(1-p)^k$, etc.  Write all your answers in detail using those formulas. - - * '''Exercise 5:''' Let $X$ follow the hypergeometric probability distribution with $N=52$, $n=10$, and number of "hot" items 13.  Use SOCR to graph and print this distribution. - - Below you can see a snapshot of the distribution of $X \sim hypergeometric(N=100, n=15, r=30)$ - - -
[[Image: SOCR_Activities_Christou_hypergeometric.jpg|600px]]
- - - * '''Exercise 6:''' Refer to exercise 5.  Use SOCR to compute $P(X=5)$ and write down the formula that gives this answer. - - * '''Exercise 7:''' Binomial approximation to hypergeometric:  Let $X$ follow the hypergeometric probability distribution with $N=1000, \ n=10$ and number of "hot" items 50.  Graph and print this distribution. - - * '''Exercise 8:''' Refer to exercise 7.  Use SOCR to compute the exact probability: $P(X=2)$.  Approximate $P(X=2)$ using the binomial distribution.  Is the approximation good?  Why? - - * '''Exercise 9:''' Do you think you can approximate well the hypergeometric probability distribution with $N=50, \ n=10$, and number of "hot" items 40 using the binomial probability distribution?  Explain. - - -
- * SOCR Home page: http://www.socr.ucla.edu - - {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_CommunityPortal_Events_May2007}} - - - - - - - - - - -
- * [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Events_May2007 Back to the SOCR USCOTS 2007 Breakout session] - * [http://wiki.stat.ucla.edu/socr/uploads/d/d5/SOCR_CAUSEwayWorkshopFlier_Apr2007.pdf SOCR/CAUSEway Workshop Flier] ([[SOCR_Events_Aug2007 | Aug. 06-08, 2007, UCLA]]) - * [[SOCR_EduMaterials_GuidelinesWikiEditing | SOCR Wiki Resource Editing Guide]] - * SOCR Home page: http://www.socr.ucla.edu {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_CommunityPortal_Events_May2007}} {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_CommunityPortal_Events_May2007}}

## SOCR Events-Specific Community Pages SOCR/USCOTS May 2007 Pages

Please try to keep these pages as clean and hierarchically organized as possible. Refer to the SOCR Editing Guide before you begin contributing to these resources.