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
1. Let X ~ U[0; 1]. Find the PDF of each of the following: (a) X^3 - 3X; (b) (X - 1/2)^2 2. Let X ~ U[0; 1]. Find the PDF of ln ln 1/X .
Let the joint pdf of X and Y be , zero elsewhere. Let U = min(X, Y ) and V = max(X, Y ). Find the joint pdf of U and V . 12 (x+y), 0< <1,0 y<1 f (x, y) 12 (x+y), 0
Let X and Y ~U(0, 1]. X and Y are independent a) Find the PDF of X+Y b) Suppose now X~(0, a] Y~(0,b] and . Find the PDF of X+Y Ο <α<b
Let Xi, , Xn be a sample from U(0,0), θ 0. a. Find the PDF of X(n). b. Use Factorization theorem to show that X(n) is sufficient for θ. C. Use the definition of complete statistic to verify that X(n) is complete for θ.
Please Answer both part a and b clearly. U(0, 1). Find the pdf of Y = X 1. (a) Let X 1+X (b) State the name of the distribution of Y in each of the followings and identifying its parameters. (i) Let X~N(0, 1) and Y = oX + . (ii) Let X~ = X2. N(0, 1) and Y (iii) Let X Exp(A) and Y =.
Please explain Let Z N(0,1), and let X = max(Z, 0) 1. Find Fx in terms of Φ(t). Ís X a continuous random variable ? 2. Compute p(X0) 3. Compute E(X) . Find the PDF fxa(u) 5. Compute V(X) (Hint: use fxa found above Let Z N(0,1), and let X = max(Z, 0) 1. Find Fx in terms of Φ(t). Ís X a continuous random variable ? 2. Compute p(X0) 3. Compute E(X) . Find the PDF fxa(u) 5. Compute...
2. Let X have the pdf Ix(x) = .. ti, 0 < x < 2. Find the pdf of Y X2/2 and P(0 <Y < 1).
Only 1-3) ,X, be a random sample from N(u,0") and let X and S be sample 1. Let mean and sample variance, respectively. In order to show that X and S are independent, tollow the steps below. x - x -X, and show the joint pdf of ,X,,..., X 1-1) Use the change of variable technique is (n-1)s n-u) еxp f(X,x 2a 20 av2n Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(4, /n), and...
Only 1-3) ,X, be a random sample from N(u,0") and let X and S be sample 1. Let mean and sample variance, respectively. In order to show that X and S are independent, tollow the steps below. x - x -X, and show the joint pdf of ,X,,..., X 1-1) Use the change of variable technique is (n-1)s n-u) еxp f(X,x 2a 20 av2n Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(4, /n), and...