I have finished the first year of my Masters in Mathematics from a German university. The area that I intended to write my masters thesis in was in Differential Geometry. However, I have decided that I would not want to pursue a career in academia in the future, or at least not one in pure mathematics. I want to get a PhD in statistics from a top US university.
Is it a good decision for me to switch my major to Probability Theory and Stochastics? This would involve another year of coursework, thus making my masters 3 years instead of 2 years. Will this be reflected negatively on my grad school application? Will they think that if I couldn't complete my masters in 2 years, how can I complete my PhD in 4-5 years?
I have done well in a rigorous Stochastic Processes course in my first year of masters and I did well in 3 statistics courses and a couple of baby probability courses in my undergrad. I might also get to be a TA for the stochastic processes course next year.
The other alternative is that I start my thesis in Differential Geometry and then apply for a PhD in statistics. When doing so, I'm afraid that I won't be getting recommendation letters for a statistics program from my pure math professors. Are my fears valid?