Insurance Strats Summer Internship

Phone Interview step:
30 mins phone interview. Let me briefly go through my resume for 5 mins or less, introduced their department (GSAM Insurance Department) for 5 mins or less, then technical questions.
Q1: The variance of a portfolio
Q2: The range of a swap rate

Superday:
5 interviewers, 30 mins each. All briefly went through my resume for 5 mins or less, then technical questions.
The questions are based on resume, they looked at my resume, and pull out some questions according to the experience they are interested in.

Interviewer 1 (a VP holding Masters degree with 16 years work experience):
Q1: Given duration, calculate portfolio value change (in a real-world setting). You'll need to identify what's the company's asset and liability, and they have different size and duration
Q2: Would the company result a profit or loss given an interest rate change
Q3: Explain the effect of interest rate's effect on option

Interviewer 2 (an Associate holding Masters degree with 5 years work experience):
Q1: What is covariance stationary in time series, use equation to explain
Q2: Calculate the premium of a limited pay term life insurance
Q3: Discussed many issues in linear regression, including auto-correlation etc

Interviewer 3 (a MD holding Ph.D in Physics at Harvard with 8 years work experience):
We discussed for about 10 mins on one of my previous TA experience, that's why he only had time to ask 1 question.
Q1: Given a random number generator that generate 1,2,3,4,5 only, produce a generator that generate 1,2,3,4,5,6,7. And expected value of the steps taken for the generator to generate a number.

Interviewer 4 (a Strategist(maybe that's how they call analyst in this dept) holding Ph.D in Physics at CalTech with 2 years work experience):
Q1: What's VaR
Q2: 1000 coins, 999 fair, 1 heads for both sides. Pick a random 1, toss for 10 times, ends up they are all heads, what's the probability that this picked one is the unfair one.
Q3: Basically this is a binomial tree discount question, but he stated that in a very-strange-to-me setting, which made me asked him to state again before finally knew what he was asking

Interviewer 5 (a don't-know-his-title holding Ph.D in FE/Math at Princeton with 7 years work experience):
Q1: Given a random generator that generate from (0,1) interval, don't use pole coordinate system, generator a point in a circle. And it's expected times to use the generator to generate one.
Q2: A P&C insurance company has Poisson Dist of claim number and Normal Dist with only positive half of claim size. What's the total claim amount.