*Use the transformation technique* to find the density function for Y = 4X + 1. The density function for X is f(x). Your answer should be a piecewise function.
f(x) = { 4e^(-4x) 0 < x < infinity
0 elsewhere
*Use the transformation technique* to find the density function for Y = 4X + 1. The...
4. Use the distribution function technique to find the density function for Y = 2X + 3 The density function for X is f(x). Your answer should be given as a piecewise function. 2x + 1) 1<x<2 f(x) = 4 0 elsewhere =f2x+1) h 5. Use the transformation technique to find the density function for Y = 4x + 1. The density function for X is f(x). Your answer should be a piecewise function. f(x) = S4e-4x 0 < x...
*Use the distribution function technique* to find the density function for Y = 2X + 3. The density function for X is f(x). Your answer should be given as a piecewise function. f(x) = { (1/4)(2x + 1) 1 < x < 2 0 elsewhere
(3x, The joint density function of X and Y is given by 0 Sy sxs1 f(x, y) = 0, otherwise. a) Use the distribution function technique to find the distribution function of W = X-Y. For 50% of the points, you may use the transformation technique, which is longer. >) Find the probability density function of W. Find the expected value E(W). )
(1 point) Let X and Y have the joint density function f(x,y)=1x2y2, x≥1, y≥1. Let U=3XY and V=5X/Y . (c) What is the marginal density function for U ? fU(u)= (d) What is the marginal density function for V ? Your answer should be piecewise defined: if 0≤v< , fV(v)= else, fV(v)=
1. (10) Suppose the random variables X and Y have the joint probability density function 4x 2y f(x, y) for 0 x<3 and 0 < y < x +1 75 a) Determine the marginal probability density function of X. (6 pts) b) Determine the conditional probability of Y given X = 1. (4 pts)
A random variable X has probability density function given by... Using the transformation theorem, find the density function for the random variable Y = X^2 A random variable X has probability density function given by 5e-5z if x > 0 f (x) = otherwise. Using the transformation theorem, find the density function for the random variable Y = X².
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
Find the mean of X given Y = 1/2. The joint probability density function is f(x, y) for random variables X and Y. f(x, y) = { (12/7)(xy + y^2) 0 < x < 1, 0 < y < 1 0 elsewhere
Evaluate the piecewise-defined function for the given values. f(x) = 4x for x 20 - 4x for x < 0 Find f(1), f(2), f(-1), and f(-2). f(1) f(2) f(-1) = f(-2) =