2. Consider the density given by gy (y; a, B) -exp the MLEs for α and β assuming both are unknown. the andsity given I"(y re unna expe?) where , 2 Sand.. Find where y 2 B and a > 0. Find Cl
x, R(x), is defined as the probability that X>x; ie, R(x)-P(X> x). Now, suppose that X has the Negative Exponential p.d.f, Then (ii) Use Theorem 1 in order to determine the MLE of R(x; θ), on the basis of a random sample X1,…, X from the underlying p.d.f. Theorem 1 Let θ-θ(x) be the MLE of θ on the basis of the observed values x1, , xn of the random sample X1, , X, from the pdf f(", θ), θ...
Recall that if X has a beta(a, B) distribution, then the probability density function (pdf) of X is where α > 0 and β > 0. In this problem, we are going to consider the beta subfamily where α-β θ. Let X1, X2, , Xn denote an iid sample from a beta(8,9) distribution. (b) The two-dimensional statistic nm 27 is also a sufficient statistic for θ. What must be true about the conditional distribution (c) Show that T* (X) is...
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y
Exercise 8 The pdf of Gamma(α, λ) is f(x)-ra)r"-le-Az for x 0. a. Let X ~ Gamma (a, λ). Show that E( )--A for α > 1 b. Let Ux2. Show that E()for n > 2 n-2
I need help analyzing B and completing C. 1. Suppose a particle with mass m is in motion in a 1D force-field depend- ing on time only, F- F(t). Determine velocity v(t) and displacement r(t) and analyze the behavior of the particle as t 0 and t ->o0 (A) F(t) eat, t 0, 0, u(0) 0; (B) F(t) = sin(wt), and F(t) cos(wt), t,w 〉 0, x(0) u(0) = 0; (C) F(t)--t , t to, β 0, x(to) 0, u(to)...
Let Xi X, lid f(r 0) with f(r:0)-e ( e) for r > ? and ? e R. (a) Find the MLE of ? (c) Using the prior density ?(0)-e-91(0,0)( ?), find the Bayesian estimator of ?
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following: (а) 29 > 0. 2"а" and (29)" (b) x7+r (с) г а — 1/29. 0, then x> y if and only if r4 > y (d) If q (e) For 1, r4 > x" if and only if q > r. For x < 1, x4 > x* if and only if q < r.
Suppose that the budget constraint is given as: PX + PyY-M and the formulation of a utility function is given as: U(X, Y)-C2/2 + δΧαΥβ with 0 < α, β < 1 and constants C, δ > 0. Answer for following questions and show all your calculation/ proof. a. Derive the formula of income-consumption curve and draw its graph. b. Derive the demand function of good X and Y respectively as functions of income and price of good X and...