Question
A. SupposeX i N(0,5), fori= 1,2,3. Assume all these random variables are independent. Derive the value ofkin each of the following. i.P(2X 1 X 2
A. SupposeXiN(0,5), fori= 1,2,3. Assume all these random variables are independent. Derive the value ofkin each of the following.
i.P(2X1 X2> 3) = k.
ii.P(X12+ X22+ X32> k)= 0.99.
iii.P(X1< k(X22+X32)) = 0.10.
B. Suppose that the binomial distribution parameteris to be estimated byP=X/n, whereXis the number of successes innindependent trials, i.e.Pis the sample proportion of successes.
- Write down the endpoints of anapproximate100(1)% confidence interval for, stating any necessary conditions which should be satisfied for such an approximate confidence interval to be used. You should also state theapproximatesampling distribution ofP=X/n.
- Suppose we are willing to assume that0.40. What is the smallestnfor whichPwill have an approximate 99% probability of being within 0.05 of?
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An Introduction to the Mathematics of financial Derivatives
Authors: Salih N. Neftci
2nd Edition
978-0125153928, 9780080478647, 125153929, 978-0123846822
