X ~ N(theta, theta) for theta > 0.
Let U = |X|.
Find the pdf of U.
for X~Gamma(Alpha, Theta); alpha and theta >0 Find the PDF of 2(Theta)(X)
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.
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
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).