Statistics PhD Profile (I am a strange one?)

[Beokaffee]

Hi everyone, I was originally interested in pure maths and was exposed to statistics late in my career (and as you will see below my first experience with it was bad pretty rough). Anyways, here is my profile and I would appreciate any advice people have about what schools are realistic. I have been learning a lot about machine learning and find it very interesting but I am interested in a lot of things related to statistics. I think my application is very strange, I would try to address my bad grade in my statement of purpose. 

Undergrad Institution: Small liberal arts school (not well known)
Major: Math
Grad Institution: Washington State School (got an MS in math)
Graduate GPA: 3.63 
Courses/Background
Graduate Courses
Probability Theory (C), Real Analysis (A), Mathematical Statistics (A), Numerical Linear Algebra (A), Computational Statistics (A), Convex Geometry (A), Abstract Linear Algebra (B+), Functional Analysis (B+), Topology (A), Metrics and Methods (A weird intro analysis course, A), Galois Theory (A-), Graph Theory (A)

I didn't take any stats courses as an undergrad

GRE: 157V, 165Q, 5       (plan on retaking)

Research I did an REU back in 2013, we actually got published recently in the journal Involve (not too impressive but neat). I also have my masters project (it wasn't original research). 
Letters of Req
My math stats professor
My masters project adviser 
Another professor at my grad place OR my professor from my REU
Programming I am somewhat good with R and Python 
Job Experience Currently work as a data analyst for an organization studying global health (IHME if you know of it). 
Miscellaneous I did the Budapest Semesters in Mathematics program back in 2013. I only took three courses (Math problem solving, combinatorics, set theory but got A's in all of them)
Two years teaching experience at my grad institution (some programs care about you not being a really bad teacher?)

Thinking about...
University of Washington (A super reach I think but it is close to friends and family... also a really good school)
UC Davis
University of Illinois Urbana Champaign
Penn State
Oregon State (safety?)

Any help would be greatly appreciated. I have gotten some advice from my stats professor but I am worried he is being too nice. Tell me how it is!
 

Edited November 3, 2016 by Beokaffee

[StatsG0d]

I don't really think you'll need to retake the GRE, for most of those schools (maybe for Washington it would help). For the others, I think you have a very good shot at getting into a few of them. Penn State DOES consider the writing score of the GRE, and a 5 is certainly a strong score in that regard. My only concern would be your C in probability theory (was it measure theoretic?). But otherwise, your profile is very strong.

[Beokaffee]

Wow thanks a bunch for the reply Mocha! My statistics professor isn't a fresh graduate and I know statistics is growing quickly in popularity from the "big data" movement. 

The probability theory class was not measure theoretic unfortunately, it was just a tough quarter for me personally and although there is no excuse I am going to try and address it in my statement. My two statistics courses afterwards I did better so I am hoping people will be nice and appreciate my pure math background. 

[StatsG0d]

Your grade in Analysis will carry more weight anyway but it was just a thought. 

Maybe consider applying to A&M or NCSU (or some other larger state school department)