2.6.9 Let X have density function fx(x) = x/4 for 0 < x < 2, otherwise fx(x)=0. (a) Let Y = X. Compute the density function fy(y) for Y. (b) Let Z = X. Compute the density function fz(z) for Z.
WILL THUMBS UP IF DONE NEATLY AND CORRECTLY! Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
X is a positive continuous random variable with density fX(x). Y = ln(X). Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
Question 3: Let X be a continuous random variable with cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y . Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5) (a) Find the cumulative distribution function, Fy (x). (b) Find the conditional distribution Fx (x|B). the mean E[X], and variance of X Fx(xB)= E[X)= Variance (e) Sketch both Fy(x) and Fx (x|B) on the same plot. Show all important values. (d) Let the output of random variable X above be applied to a square-law device according to Y 5X2. Find the mean value of...
3. Let X.. U(-1,1) for i € {1, 2, 3). (a) Write down the expected value and variance of X,. Sketch the pdf fx. [3] (b) Let Y = X1 + X2. Compute the pdf fy of Y and sketch it. Using fy, or otherwise, compute the expected value and variance of Y. (7) (c) Let Z = X1 + X2 + X3 = Y + X3. Using exactly the same technique that you used in part (b), it can...
I am studying Continuous Random Variables. Hope can some one tell me the solutions of these two problems! II.1 Let X be a continuous random variable with the density function 1/4 if x E (-2,2) 0 otherwise &Cx)={ Find the probability density function of Z = X density function fx. Find the distribution function Fy (t) and the density function f,(t) of Y=지 (in terms of Fx and fx). II.1 Let X be a continuous random variable with the density...
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
2.9.10 Suppose X has density fX(x) = x3/4 for 0 < x < 2, otherwise fx(x) = 0, and Y has density fr (y)-5y4/32 for 0 < y < 2, otherwise fr (y)-0. Assume X and Y are independent, and let Z = X + Y (a) Compute the joint density fx.r(x. y) for all x, y e R (b) Compute the density fz(z) for 2.
2.8.14 Let X and Y have joint density fX,Y (x, y) = (x2 + y)/36 for −2 < x < 1 and 0 < y < 4, otherwise fX,Y (x, y) = 0. (a) Compute the conditional density fY|X (y|x) for all x, y ∈ R1 with fX (x) > 0. (b) Compute the conditional density fX|Y (x|y) for all x, y ∈ R1 with fY (y) > 0. (c) Are X and Y independent? Why or why not?