6.42
Let (X,Y) be a uniform random point on the rectangle
D = [0,2] * [0,3] = { (x,y) : 0<=x<=2, 0<=y<=3}.
Let Z = X + Y. find the distribution of Z (not the pair (X, Z))
6.42 Let (X,Y) be a uniform random point on the rectangle D = [0,2] * [0,3]...
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].
Let X be a random variable from a uniform distribution over [0,3]. Find the expected value of
Please do by hand. Thanks in advance.
4. Let X1 - uniform(0,3) and X2 – uniform(0,2) and suppose that Xi and X2 are independent. Find the pdf of Y1 = X1 + X2. (Hint: First find the joint pdf of Yi and Y2 = X2.)
Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set {1, 3} and Y has a discrete uniform distribution over the set {1, 2, 3}. Let V = X + Y and W = X − Y . (a) Find the PMFs for V and W. (b) Find mV and (c) Find E[V |W >0].
Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and Y being independent. Let U = X/Y and V = X. (a) Find the joint distribution of U and V . (b) Find the marginal distributions of U.
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W min(X, y.z a) Find pdf of W Find E(1-11 b)
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W min(X, y.z a) Find pdf of W Find E(1-11 b)
Let A, B, and C be independent random variables, uniformly distributed over [0,9], [0,2], and [0,3] respectively. What is the probability that both roots of the equation Ax^2+Bx+C=0 are real?
(1 point) 3. Let X and Y be random variables with a joint probability density function f(z, y)e (a)Find the marginal distribution functions of X and Y, respectively. i.e. Find f(z) and f(y) f(x)- elsewhere (b) Identify the distribution of Y. What is the E(Y) and SD(Y) E(Y)- (c) Are X and Y independent random variables? Show why, or why not (d) Find P(1 X 2|Y 1) E SD(Y)-
Let X and Y be independent uniform distributed random variables, 0 < X < 1 and 1 < Y < 2. Let Z = X + Y. What is the pdf of Z?