(11 pts) Use the Distribution Function Method here: The random variable y-Beta( Let U Y4. Find...
6. (11 pts) Use the Distribution Function Method here: The random variable ??~????????(∝= 4, ?? = 2). Let ?? = ??4. Find the pdf of U. (1 l pts) Use the Distribution Function Method here: The random variable Y~Beta(α= 4, β = 2). Let U 6. Y4, Find the pdf of U.
6. (11 pts) Use the Distribution Function Method here: The random variable Y~ Beta(o4,B 2). Let U-Y4. Find the pdf of U.
5. (11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter β. Let ?? = √??. Find the pdf of U. Note: U has a Weibull distribution. You will see the Weibull distribution many times in this course 5. (11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter B. Let U-VY. Find the pdf of U. Note: Uhas a...
(11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter B. Let U vY. Find the pdf of U. Note: Uhas a Weibull distribution. You will see the Weibull distribution many times in this course. 5.
I. Let the random variable y have an uniform distribution with minimum value θ = 0 and maximum value θ2-1 and let the random variable U have the form aY +b, where a and b are both constants and a > 0. (a) Using the transformation method, find the probability density function for the random variable U when a 2 and b-4. What distribution does the random variable U have? (b) Using the transformation method, find the probability density function...
7. (11 pts) Use the Transformation Method on this problem (be sure to verify that the function h(y) is increasing or decreasing over the domain of y, either by graphing h(y) or by using differential calculus): 7. (11 pts) Use the Transformation Method on this problem (be sure to verify that the function h(yjs increasing or decreasing over the domain of y, either by graphing h(y) or by using differential calculus): The random variable Y~Gamma(o:: 3/2,β-4). Use the transformation method...
Use the method of distribution functions 2. (5 marks) Consider a random variable Y with density function 3y2 0 ,else Find the probability density function of U 4-Y
9. (9 pts) The random variable ??~??????????(∝= 2, ?? = 4). Use the method of moment-generating functions to prove that the moment generating function for the random variable ?? = 3?? + 5 is 10. 9. (9 pts) The random variable Y-Gamma(α-2. functions to prove that the moment generating function for the random variable W mw(t)120)2 4). Use the method of moment-generating 3Y 5 is est (1-12t)2 10, (9 pts) Suppose that Y has a gamma distribution with α-n/2 for...
Use the Method of Distribution Functions 2. (5 marks) Consider a random variable Y with density function 3 v 0 .else Find the probability density function of U 4- r2
Question 1: (10 marks) Let Y, Y....,Y, be a random sample from the beta distribution with a = B = 4, and I2 = { u u = 1,2). Write the likelihood ratio test statistic A for testing Ho : H = 1 versus H:u= 2. Note that the pdf of a beta(a,b) distribution is as follows: com_(a+b)/2-1(1 - 0)8-1, 0<I<1. f(x) = f(a)(B)"