Physics Major Applying to Statistics PhD Admission Profile

[itbeliekthatsometimes]

Undergraduate - BA in Physics (Mathematics Minor) 3.7/4.0 GPA

Race: Asian (male)

GRE - Not taken yet (plan to take soon)

Research Experience: two years research in physics (chaos theory/computational fluid mechanics) during undergrad - no publication yet though

LOR: one math prof and two physics profs (one research advisor and one academic advisor)

Awards: dean's list all semesters, honors bachelors thesis on research, Sigma Pi Sigma

RELEVANT Math Courses Taken: Introduction to Statistics, Advanced Calculus, Linear Algebra, Probability, Ordinary and Partial DE, Computational Mathematics (somewhat similar to numerical analysis).

Maybe Relevant Physics: Statistical Physics, Mathematical Physics, Quantum Mechanics??

Concern: I heard Real Analysis is essential for applying to Statistics graduate programs, but I was not able to fit it in my schedule when I decided to pursue Statistics grad school... I also did not do too well in Probability course (B+) due to a health issue during finals... Would it be better to do a masters to improve my GPA and research experience in Applied Probability/Statistics? I just don't know how I will be compared with others coming with math and statistics degrees.

Tentative List of Programs (Statistics PhD):

Stanford 

UC Berkeley

U Michigan 

UIUC

U of Washington

StonyBrook (SUNY)

UCLA

UCSB

UCD

UCSD

UCI

(most of them are UCs since I want to stay in Cali if possible) I would appreciate any recommendation to the list or if I should pursue Masters or PhD 🙂 Thanks.