Fisher information for Cauchy location family. Suppose X₁, X2,..., Xn iid with pdf 1 f(x | 0) = π(1 + (x −0)²)* Let X = (X₁,..., Xn), X~ f(x | 0). Find Ix (0).
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- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.The number of defects on the front side (X) of a wooden panel and the number of defectsa on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy(x,y)=c(x+y), x= 1,2,3 and y=1,2,3. Determine the value of c.The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3.Determine the marginal pmf of X. Determine the conditional pmf of Y given X=2.
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