SOCR EduMaterials Activities Discrete Distributions
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Revision as of 02:06, 22 October 2006
\item[a.] 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: \\ $X \sim b(10,0.5)$, find $P(X=3), E(X), sd(X)$, and verify them with the formulas. \\ $X \sim b(10,0.1)$, find $P(1 \le X \le 3)$. \\ $X \sim b(10,0.9)$, find $P(5 < X < 8), P(X < 8), P(X \le 7), P(X \ge 9)$. \\ $X \sim b(30,0.1)$, find $P(X > 2)$. %Below you can see the distribution of Failed to parse (unknown function\math): X \sim b(20,0.3) <\math> \item[b.] 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 the distribution of <math> X \sim geometric(0.4) <\math> \item[c.] Select the geometric probability distribution with $p=0.2$. Use $SOCR$ to compute the following: \begin{itemize} \item[1.] $P(X=5)$ \item[2.] $P(X > 3)$ \item[3.] $P(X \le 5)$ \item[4.] $P(X > 6)$ \item[5.] $P(X \ge 8)$ \item[6.] $P(4 \le X \le 9)$ \item[7.] $P(4 < X < 9)$ \end{itemize} \item[d.] Verify that your answers in part (c) agree with the formulas we 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. \item[e.] 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 the distribution of <math> X \sim hypergeometric(N=100, n=15, r=30) <\math> \item[f.] Refer to part (e). Use $SOCR$ to compute $P(X=5)$ and write down the formula that gives this answer. \item[g.] 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. \item[h.] Refer to part (g). Use $SOCR$ to compute the exact probability: $P(X=2)$. Approximate $P(X=2)$ using binomial distribution. Is the approximation good? Why? \item[i.] 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. \end{itemize} <hr> * SOCR Home page: http://www.socr.ucla.edu {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}
