for X~Gamma(Alpha, Theta); alpha and theta >0 Find the PDF of 2(Theta)(X)
X ~ N(theta, theta) for theta > 0. Let U = |X|. Find the pdf of U.
Let X1, X2, ... be a random sample from the pdf f(x) = 1/theta e-x/theta, find the likelihood ratio (LR test of H0: theta = thetao vs H1:theta >theta0
f(y)= 3y^2/theta^3 from 0<y<theta, o otherwise. a) Find the pdf of Y(n)= max(Y1,Y2,...,Yn) b) if n=11 find E(Y(n)) c) if n=11 find the pdf of the median
Let X1...Xn be a random sample from a continuous distribution with Lomax PDF with gamma=2 a) determine the maximum likelihood estimator of alpha b) determine the estimator of alpha using the method of moments
Let X have a gamma distribution with alpha=4, and beta=3. Find P(9<X<27).
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
2. Let X have the pdf Ix(x) = .. ti, 0 < x < 2. Find the pdf of Y X2/2 and P(0 <Y < 1).
hint : solve the cubic equation for theta and then plot the graph
of theta vs q for all combinations of gamma and alpha.
80²+(1-9)0 - qx = 0 q = 0:0.01:2 (0 > 2 with steps of 0.01] X = 0,5,8,12 8 -0.05, 0.1,0.15 Plot a curve for ous q for all possible (12) combinations of X and 8 using MATLAB
Please answer the following question and show every step. Thank
you.
Let Xi,..,Xn be a random sample from a population with pdf 0, x<0, where θ > 0 is unknown. (a) Show that the Gamma(a, b) prior with pdf 0, θ < 0. is a conjugate prior for θ (a > 0 and b > 0 are known constants). (b) Find the Bayes estimator of θ under square error loss. (c) Find the Bayes estimator of (2π-10)1/2 under square error...
Consider the hierarchical Bayes model (a) Show that the conditional pdf g(ply, 0) is the pdf of a beta distribution with parameters (b) Show that the conditional pdf g(θ|y, p) is the pdf of a gamma distribution with parameters 2 and log p
Consider the hierarchical Bayes model (a) Show that the conditional pdf g(ply, 0) is the pdf of a beta distribution with parameters (b) Show that the conditional pdf g(θ|y, p) is the pdf of a gamma distribution...