assuming x is par(2) calculate P(Y<2) if Y=X^2 X=Pareto(2) Calculate P(Y<2) if Y=X^2
Let X ~Par (2) and Y = ln(X). Compute P(Y > 1).
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
calculate 80th percentile of Par(3) Calculate 80th percentile of Pareto(3) Choices 1.7 2.5 1.4 2.4
a) calculate the slope across arc AB, assuming that at point A
x = 2 and y = 9 and that point B x= 4 and y = 6
b) calculate the slope across arc BC, assuming that at point B
x = 4 and y = 6 and that at point C x = 8 and y = 3
C) calculate the slope across arc CD , assuming that at point
C x = 8 and y=3 and that...
12. Suppose XIX, iid X, P(θ, l), where P(0,1) is the one-parameter Pareto distribution with density f(x)-0/10+1 for l < x < 00, Assume that θ >2, so that the model θ/(0-1)(8-2)2 (a) obtain the MME θι from the first moment equation and the MIE θ2 (b) Obtain the asymptotic distributions of these two estimators. (c) Show that the ML is asymptotically superior to the MME P(0,1) has finite mean θ/(9 -1 ) and variance
Assuming X has distribution U(5,15) Calculate P(X>9)
let X=pareto(α,γ) find the distribution and density function of Y=logX
The random variable X is distributed as a Pareto distribution with parameters α = 3, θ. E[X] = 1. The random variable Y = 2X. Calculate V ar(Y )
let x and y be continuous random variables with joint probability density function f(x,y)=(1/2)xy+(1/2)x calculate P(Y<X|X=1) A) 5/12 B) 3/4 C) 1 D) 2 E) 4
Question 2 Let X Pareto(r, 8 = 1) which has pdf: f(x) = 1 , 1 >1 and r > 1 (a) Given a random sample of size n from X show that the mle for r is: r* = 1/7 where Y = SEY and Y = log X (b) Let Y = log X Use the mgf technique (with t <r) to show that: Y Exp(1 = r) [ HINT: My(t) = Eletbox] = E[X“) = * **f(x)dt...