Question #1 (statistics)
You can also do a QQ plot where you compare the distribution against a normal distribution, draw a line through you the points plotted. If all your points lie on this straight line then your distribution is normal. This is gives you a visual of normality, also you can see if there are left or right tails, or you can compute the Jarque-Bera test, if JB > 6 , -> distribution is not normal, if JB < 6 -> distribution normal
Question #4 (probability theory)
You'll win 2/3 of the time if you switch
Question #19 (finance)
VaR measures how much you could loose over a certain period of time with a certain confidence level.
Distribution of returns are covariance stationary -> ie mean and variance are constant over time
Market returns are normal and iid over time
It depends. If A and B are independent then Cov(A,B) = 0 , so you have VaR(A+B) = VaR(A) + VaR(B) else if Cov(A,B) != 0 then VaR(A+B) = VaR(A) + VaR(B) + 2Cov(A,B)
