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 support (0, 1) and PDF defined by...
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
4. et X be a continuous random variable with support (0, 2) and PDF defined by f(x) = ( cx3 0 < x < 2 0 otherwise. a) Compute E[X]. b) Compute V ar(X)
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).
4. (20%) Let X be a continuous random variable with the following PDF Sce-4x 0<x fx(x) = to else where c is a positive constant. (a) (5%) Find c. (b) (5%) Find the CDF of X, Fx(x). (c) (5%) Find Prob{2<x<5} (d)(5%) Find E[X], and Var(X).
2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a) Find the CDF Fx (x). (b) Suppose 2 =9(X), where gle) = { " Find the (DF, PDF of
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3) Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
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 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...
3.17 A PDF for a continuous random varaiable X is defined by C 0<x<2 2C4<< 6 fx(x) = 3 C 7<<<9 0 otherwise where C is a constant. (a) Find the numerical value of C. (b) Compute Pr[1 < X < 8). (c) Find the value of M for which "fx(s)de = [fx (a)dr = 1 J-00 Mis known as the median of the random variable.