33.- Let X1,..., Xn a random sample of the population with Gamma(a, ß) distribu- tion whose density function is 1 f(r; a, B) le=#/B I(@)Ba' with a > 0, B > 0 and 0 < x <∞. Show that if a = 1, S(X) = ", X; is a sufficient statistic for B. b) Show that if ß is known, S(X)= II"_, X; is a sufficient statistic for a. c) If a and B are unknown, obtain a sufficient (two-dimensional) statistic for the parameters (a, B).

33.- Let X1,..., Xn a random sample of the population with Gamma(a, ß) distribu- tion whose density function is 1 f(r; a, B) le=#/B I(@)Ba' with a > 0, B > 0 and 0 < x <∞. Show that if a = 1, S(X) = ", X; is a sufficient statistic for B. b) Show that if ß is known, S(X)= II"_, X; is a sufficient statistic for a. c) If a and B are unknown, obtain a sufficient (two-dimensional) statistic for the parameters (a, B).

Name: 33.- 33.- Let X1,., Xn a random sample of the population with Gamma(a,
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 33.- 33.- Let X1,., Xn a random sample of the population with Gamma(a, B) distribu-tion whose density function is1-xª-1e-x/ßI(@)Baf(x; a, B)with a > 0, ß > 0 and 0 < x <∞.a) Show that if a = 1, S(X) = X; is a sufficient statistic for B.b) Show that i

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

See similar textbooks

Similar questions

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
Differentiate. f(w) = w / [w + (d/w)]
Let the density function of a random variable X be given by fx(x) = 0x®-', 0
Let m(t) =(1/6)e^t+(2/6)e^2t+(3/6)e^3t Find E(y) Find V(y) Find the distribution of y
6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left headlight) and Y (the right headlight) ze(y+1) for r> 0.y > 0 f(x, y) 0 otherwise (a) What is the probability that the lifetime X of the left headlight exceeds 2.8? (b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer (c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?
Find the slope of * y + Vx+ y =x at (3,1).
Suppose that X₁ and X₂ have joint probability density finn 1x₁x2, if 1
Let f(x) is density function of continuous random variable x then the (expected value E(x Ek) = [ xfx)dx Ew) = [_fx)dx - 00 Ek) = ] -xfx)dx Ex)= | xf(x)dx
2. Let X be a Chi-squared random variable with density function fx(x) = exp (-;), a x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = VX. Show that the density function of Z is given by Sale) = 2a exp (-) z > 0. Hence state the value of a.
A random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is given by: ´ayf f(y) = {ya+1 (0, if y > yo elsewhere ii) ayg (a-2)(a-1)2" Show whether or not that the variance of Y is
Let X and Y be two continuous random variables with joint probability density [3x function given by: f(x,y)= 0
Show that the gamma density function with parameters a > 1 and A > 0 has a relative maximum at :={(a-1)