Help with Biostat quals in 3 months

[Biostatqual]

Hi I am in my 2nd yr of doctorate program in Biostat in a top 20 US institute. I took my written quals last yr and did not get through. I have my 2nd attempt in 3 months and want to get though this time. Last time I struggled with large sample theory; not much has changed this year. Still struggling with proofs like show X_n+Y_n converges as/p to x+y if x_n converges to x(in p/as) yn converges to y(in p/as). Basically need help on how to get better in measure theory proofs. Showing convergence for increasing and decreasing sets and so on. 

 

[BayesianLove]

This is why I plan to take Intro to Real Analysis during my first year. I'm coming with no background with proof-based math and I've got to get ready for second year (measure theoretic probability).

[bayessays]

It sounds like you already know what topics you need help on, so I'd search for course notes on those exact topics. I've often found that you can find a professor who will have written notes that just "click" more than other texts. Other than that, I'd say work through lots of solutions until you understand every step, literally memorize them if you need to, and then start working on similar practice problems. 

[StatsG0d]

I agree with @bayessays, but I would add it might be worthwhile to look at some sequences stuff in real analysis, too. Make sure you understand that material thoroughly before you jump to the measure theory stuff.