Let X be a random variable with support Sx = [−6, 3] and pdf f(x) = 1/81x^2
for x ∈ SX , 0 otherwise.
Consider the random variable Y = max(X, 0). Calculate the CDF of Y , FY (y), where y is any real number.
Let X be a random variable with support Sx = [−6, 3] and pdf f(x) =...
(10 points) Let X be a random variable with support Sx = (-6, 3) and pdf f(x) = $1x2 for ce Sx, zero otherwise. Consider the random variable Y = max(x,0). Calculate the CDF of Y, Fy(y), where y is any real number.
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
Let X be a random variable with pdf S 4x3 0 < x <1 Let Y 0 otherwise f(x) = {41 = = (x + 1)2 (a) Find the CDF of X (b) Find the pdf of Y.
1. Let X be a continuous random variable with support (0, 1) and PDF defined by f(x) = ( cxn 0 < x < 1 0 otherwise, for some n > 1. a) Find c in terms of n. b) Derive the CDF FX(x).
1. Let X be a continuous random variable with CDF F(ro)-a+b 3 and support set 0, 1]. (a) Calculate the values of a, b that would make F(ro) a valid CDF. (b) Write out the pdf of X. c) Calculate EX d) Calculate EX
Problem # 8. a) Let X be a continuous random variable with known CDF FX(x). LetY = g(X) where g(·) is the so-called signum function, which extracts the sign of its argument. In other words, g(X) = { -1 x<0, 0 x=0, 1 x>0 } Express the PDF fY (y) in terms of the known CDF FX(x). b) Let X be a random variable with PDF: fX(x) = { x/2 0 <= x < 2, 0 otherwise} Let Y be...
Let X be a random variable with PDF fx(X). Let Y be a random variable where Y=2|X|. Find the PDF of Y, fy(y) if X is uniformly distributed in the interval [−1, 2]
Let X and Y be a random variable with joint PDF: f X Y ( x , y ) = { a y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise What is a? What is the conditional PDF of given ? What is the conditional expectation of given ? What is the expected value of ? Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Let X and Y be a random variable with joint PDF: fxx (x, y) = { 1, 2 > 1,0 Sysi 0 otherwise 1. What is a? 2. What is the conditional PDF fy|x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.