5. Consider the Clayton copula: C(u,v) = (u¯ª +v¯ α>0 -a - a for 0≤u≤1, 0≤v≤1, a. Show that the marginal distributions for u and v are uniform. b. Show that the pdf for this copula is always non-negative. c. Find the lower tail dependence, defined as λ₁ = lim Pr[X ≤ Fx' (u)|Y ≤ Fy'(u)] = u→0+ +0

A recent survey of 1030 U.S. adults selected at random showed that 627 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.

Previous surveys indicate 33% of households in Barrie regularly recycle household waste through a blue box program. In a random sample of ten households, what is the probability of finding exactly five who regularly use a blue box?

Question b