Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem , and some problems will require more than one application of L’Hôpital’s rule. 60. lim x → 0 e 2 x − 1 − 2 x − 2 x 2 x 3
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem , and some problems will require more than one application of L’Hôpital’s rule. 60. lim x → 0 e 2 x − 1 − 2 x − 2 x 2 x 3
Solution Summary: The author evaluates the value of the limit undersetxto 0mathrmlime.
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
A random variable X takes values 0 and 1 with probabilities q and p, respectively, with q+p=1. find the moment generating function of X and show that all the moments about the origin equal p. (Note- Please include as much detailed solution/steps in the solution to understand, Thank you!)
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
Chapter 4 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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