Oxford MCF 面经 [2016-02-25]

2月25日面的 OX， 面试的Professor是 Hanqing Jin。人很 Nice，然后带着一个PHD。面试问题比较基础，好好准备还是可以回答出来的

1. Definition of continuity

2. For function f(x)=0 if x is irrational f(x)=1/p if x is rational x=q/p f(x)=0 x=0
   问是不是cts function

3. what is a random variable, what is a measurable space

4. X - standard normal distribution 求E(X)

5. PDE 求wave equation solution.

另一个小伙伴的interviewer 是Sam Cohen

问的是

1. Introduce yourself
2. have you studied anything related to stochastic process? I said yes, then he followed up with have you studied brownian motion? Then we briefly talked about levy's construction. (Prepared to answer questions related to Brownian Motion if you have completed this module)
3. Define different types of convergence. I answerd uniform, pointwise and converges in Lp. Definition for each of them. What their relationships? Give me an example pointwise convergence does not imply Lp convergence. Prove Lp implies pointwise covergence. Prove Uniform implies Lp. Definition of covergence in measure. Prove convergence in Lp implies covergence in measure. For all the examples, he aksed me to start with function with domain (0,1), then generalise to R.
4. Have you studied apply statistics? Define confidence interval. Explain intuitively.

Hope you guys will find it helpful. Good luck with future interviews!

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