Please do by hand. Thanks in advance.
Please do by hand. Thanks in advance. 4. Let X1 - uniform(0,3) and X2 – uniform(0,2)...
Please do by hand. Thanks in advance. 5. Let X1 and X2 have joint pdf f(x1, x2) = 4xı, for 0 < x < x2 < l; and 0 otherwise. Find the pdf of Y = X/X2. (Hint: First find the joint pdf of Y and Y2 = X1.)
Please do by hand. Thanks in advance. b and c below are a part of the problem. 3. Let Xi and X2 be independent random variable, each following an exponential(1) distribution. Define new random variables Y = X1 - X, and Y2 = X1 + X2. a) Find the joint pdf of Y and Y2. b) Find the marginal pdf of Yı c) Find the marginal pdf of Y2
12. (8 Pts.) Let Xi and X2 have the joint PDF Let Yi Xi/X2 and Y2 = Xy. Find the joint PDF of(H.)a). Are Y1 and Y2 independent?
Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y; be the partial sums, i.e., Y1 = X1, Y2 = X1 + X2, Y3 = X1 + X2 + X3. 1. What is the distubution for each Yį, i = 1, 2, 3? 2. What is the expected value for Y1 + Y2 +Yz? 3. Are Yį and Y2 independent? Explain it by computing their joint P.M.F. 4. What is the variance of Y1...
7. Let X1 and X2 be two iid exp(A) random variables. Set Yi Xi - X2 and Y2 X + X2. Determine the joint pdf of Y and Y2, identify the marginal distributions of Yi and Y2, and decide whether or not Yi and Y2 are independent [10)
thanks Suppose that Xi and X2 are independent random variables each having PDF: : otherwise (a) Use the transformation technique to find the joint PDF of Yi and Ya where Y-X1 and ½ = Xi +X2. (b) Using your answer to part (a), and the fact that o Vu(1-u) find and identify the distribution of Y2.
4 points) Let X1, X2 be independent random variables, with X1 uniform on (3,9) and X2 uniform on (3, 12). Find the joint density of Y = X/X2 and Z = Xi X2 on the support of Y, Z. f(y, z) =
Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 = X(1), and Yk = X(k) – X(k-1), 2<k<n. Find the joint pdf of Yı,Y2, ...,Yn. Hint: Note that (Y1,Y2, ...,Yn) = g(X(1), X(2), ..., X(n)), where g is invertible and differentiable. Use the change of variable formula to derive the joint pdf of Y1, Y2, ...,Yn.
(a) Write down the joint pdf of X1 and X2. [4] (b) By using the transformation of random variable method, find the joint pdf of Y1 = X1 and Y2 = X2/X1. [16] (c) Hence find the marginal pdfs of Y1 and Y2. [8] (d) Compute the covariance between Y1 and Y2, cov [Y1, Y2]. [8] (e) State, with justification, whether Y1 and Y2 are independent.
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.