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Clayton copula model: Denote by τ1, . . . , τm the default times of m companies. Assume that the τi are exponentially distributed with parameters λi, i = 1, 2, (P (τi ≤ t) = 1 - exp(-λit)) and that they follow a copula model with Clayton copula with parameter θ.
a) Write down the joint survival function and the corresponding mixture represen- tation explicitly.
b) Assume that you have a random number generator that is able to generate in- dependent Gamma distributed and uniformly distributed random variables. Write down an algorithm to generate a sample of τ1, τm via the mixture distribution.
c) Assume that λ1 = ... = λm. Write down
limθ→∞ P (τ1 ≤ T, τm ≤ T ) and limθ→0P(τ1 ≤ T, τm ≤ T ).
A particle moves along a number line such that its position s at any time t, t(greaterthan or equal to), is given by s(t)=2t^3-15t^2+24t+1. A) Find the average velocity over the time interval [1,2].
The police department of a major city has found that the average height of their 1,200 officers is 71 inches (µ = 71 in.) with σ = 2.6 inches. What is the z score for an officer who is 72 inches tall? Based on the z score and the z table, what is th..
4. Consider a glass factory that can produce four different kinds of glasses: beer, wine, drinking, and schnapps. Glass manufacturing uses machine hours, labour, and sand as its main inputs.
Suppose that X is not orientable. Prove that X*Y is never orientable, no matter what manifold Y may be. (Hint: First show that X * R^L is not orientable. But every Y has an open subset diffeomorphic to R^L.)
Define portion, rate, and base. Create an example using Walt Disney World to show when the portion could be larger than the base.
State and prove the Squeeze Theorem for sequences. Use it to prove that limn→∞(n2 + n + 48769504 + sin(n)/n4 + πn2 - 2) = 0
A rectangular box has a height of 4 feet to within an accuracy of 1 in and a square base with width 2 feet to within an accuracy of 1 in. Find the volume V and the approximate error dV in the volume of the can.
when heated a metal bar expands by 0.4%. if the lenght of the bar is 1cm, what was the orignial length of the bar?
The ________ environment includes the actors involved in producing, distributing, and promoting an offering. The main actors are the company, suppliers, distributors, dealers, and the target customers.
Calculate the marginal product for the following levels of man-hours: 50, 100, 150; 200; 250 and 300. Comment on the results.
Digital information can be represented through the use of Boolean algebra, which is an important concept to study if one wishes to understand how computers work.
If a design life of 10 yr with a reliability of 0.99 is required, what should the system MTTF and median time to failure be? If each component has a CFR, what will the component MTTF and median time to failure be?
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