1-Calculate the pdf of y given that the pdf of x is given by pdf x
2- cketch of pdf
1-Calculate the pdf of y given that the pdf of x is given by pdf x...
#5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1 #5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1
1. (20 points) Consider a random variable X with PDF and a random variable Y with PDF o)(350 e ys0 Given thatX and Y are independent, find the PDF of Z = X + Y. 1. (20 points) Consider a random variable X with PDF and a random variable Y with PDF o)(350 e ys0 Given thatX and Y are independent, find the PDF of Z = X + Y.
Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
Determine the pdf of the random variable Y, where Y=X^2. Given that c=6/7 1. A random variable X has the density function f(x)- otherwise. 1. A random variable X has the density function f(x)- otherwise.
Calculate the following for the random vector (XY) with joint pdf fixy)--(3/4)(x+y) if 2x<yco, -1<x<o. 1. The marginal pdf of X and the marginal pdf of Y. Are X and Y independent random variables? 2. The expected value and variance of X and Y respectively. 3. The joint cdf in the case 2x<y<0. -1<x<0. 4. The expected value of the random variable Z defined as X^2 times Y^2. 5. The covariance between X and Y. 6. The expected value and...
Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y)
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours. Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/ x , if 0 < x < 1, 0 < y < x f(x, y) =0, otherwise . Find the covariance of the random variables X and Y . 2.Let X1 be a Bernoulli random variable with parameter p1 and X2 be a Bernoulli random variable with parameter p2. Assume X1 and X2 are independent. What is the variance of the random variable Y...
The PDF of random variable X and the conditionalPDF of random variable Y given X are fX(x) = 3x2 0≤ x ≤1, 0 otherwise, fY|X(y|x) = 2y/x2 0≤ y ≤ x,0 < x ≤ 1, 0 otherwise. (1) What is the probability model for X and Y? Find fX,Y (x, y). (2) If X = 1/2, nd the conditional PDF fY|X(y|1/2). (3) If Y = 1/2, what is the conditional PDF fX|Y (x|1/2)? (4) If Y = 1/2, what is...