Recent content by Mogarrr

Ok, there is a relationship between the Gamma and Poisson distribution. Let X \sim Gamma(\alpha, \beta) , then P(X \leq x) = P(Y \geq \alpha) , where Y \sim Poisson(x/\beta) . Now let p > q , p,q \in \mathbb{Z}^{+} a>0 , then P(X^2_{p} > a) < P(X^2_{q} > a) \Leftrightarrow P(Y > p) < P(Y...

Oops. Should have written X^2_{n} = \sum^{n}_{i=1} Z^2_{i} . I was thinking that since the Z_{i}'s are identically distributed, that I could just sum up their squares, X^2_1 . Why am I wrong here, if they're identically distributed? I will try the direct method, since X^2_{p} \sim \Gamma(p/2...

Based on your hint, here's what I'm thinking... Well, then, if Z_{i} \sim N(0,1) (and i.i.d.) , and X^2_{n} = \sum_{i=1}^{n} Z_{i} , then X^2_{p} = pZ^2_1 and X^2_{q} = qZ^2_1 . Thus for all a , P(X^2_{p} > a) = P(pZ^2_1 > a ) = P(Z^2_1 > \frac {a}{p}) \geq P(Z^2_1 > \frac {a}{q}) =...

Homework Statement Prove that the X^2 distribution is stochastically increasing in its degrees of freedom; that is if p>q, then for any a, P(X^2_{p} > a) \geq P(X^2_{q} > a), with strict inequality for some a. Homework Equations 1.(n-1)S^2/\sigma^2 \sim X^2_{n-1} 2.The Chi squared(p) pdf is...

Thanks for the pep talk.

Since I couldn't find any publications by a few mentors, I decided to test "contacting a mentor", by simply introducing myself, stating my research interests, my interest in their project, and asking whether my interests were related to their project. I tried this with one mentor, emailing them...

Homework Statement Using rep() and seq() as needed, create the vector 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 5 6 7 8 9 Homework EquationsThe Attempt at a Solution I figured out that seq() only takes numbers for the 'from' and 'to' arguments, since I tried seq(seq(...)). Also, I'm not...

That sounds good. Thanks for the idea.

Greetings forum-goers, I am planning to apply for a DHS summer internship, where I am encouraged to contact research mentors (although it's stated that OSRI makes the hiring decision). I plan on cold emailing several mentors and, besides introducing myself and mentioning how I am interested in...

I have an exact test for small samples, however I wanted to talk about one more thing concerning this problem. I just learned that McNemar's test can be viewed as a within Chi-Squared Test. Do you think this data is an example of a within-subject design?

Homework Statement 10.24 Is there any relationship between the type of treatment and the response? What form does the relationship take? Here's that data (column variables are responses): \newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{|c|c|c|c|c|} \hline Treatment & +Smear &...

Homework Statement Refer to Table 2.11. 10.6 What significance test can be used to assess whether there is a relationship between receiving an antibiotic and receiving an antibiotic culture while in the hospital? Here's my attempt of recreating the table: \newcommand\T{\Rule{0pt}{1em}{.3em}}...

Thanks guys. Actually, I switched the example to 2 closed balls that just touch each either in \mathbb{R}^2 and to show this was connected, I just looked at a line that intersects the disconnections, and then showed how there can't be a disconnection there.

Then, I'd have to show the closed circle in \mathbb{R}^2 is connected. But I'm not really sure how to do that? I suppose a proof by contradiction, assuming the closed circle is disconnected... (that's pretty much the only technique I got when it comes to connected sets). I suppose if any 2 of...

Homework Statement This is from Baby Rudin Exercise 2.20- Are closures and interiors of connected sets always connected? (Look at subsets of \mathbb{R}^2 ). Homework Equations The interior is the set of all interior points for a set E that is a subset of a metric space X. A subset Y of a...