a. Find the cdi and pdf of Y in terms of the cdf and pdf of X 3 pt. b. Find the pdf of Y when X is a Gaussian random variable with zero mean and unit variance 3 pt.
2 pts 5 pt. Find the cdf and pdf of Y in terms of the e Find the pdf of Y w df and p df of X - -L hen X is a Gaussian random variable with zero mean and varia ㄟ ill he heavy
Let Y-ar+b (a) Find the mean and variance of Y in terms of the mean and variance of X b) Evaluate the mean and variance ofY if Xhas the following PDF: (a)-ele (c) Evaluate the mean and variance of Y if Xis the Gaussian random variable with mean 0 and variance d) Evaluate the mean and variance of Yif X-bcos 2U) where U is a uniform random variable in of 1 the unit interval. Let Y-ar+b (a) Find the mean...
Problem1 Let Y=aX + b . (a) Find the mean and variance of Y in terms of the mean and variance of X (b) Evaluate the mean and variance ofYifXhas the following PDF (c) Evaluate the mean and variance of Y if Xis the Gaussian random variable with mean 0 and variance of 1 d) Evaluate the mean and variance of Yif X bcos(2RU) where U is a uniform random variable in the unit interval. Problem1 Let Y=aX + b...
Question 6 A random variable X has cdf χ20 Plotthe cdf and identif.,(x)-1-0.2~ a) Plot the cdf and identify the type of the random variable. b) Find the pdf of X. c) Calculate P[-4eX<-1], P(xS2], P(X=1], Pf2-K6], and P[X>10]. d) Calculate the mean and the variance of X. If the random variable X passes through a system with the following chara cteristic function: e) f) Find the pdf of Y. Calculate the mean and the variance of Y. Good Luck
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)?...
a) Let X and Y be two random variables with known joint PDF Ir(x, y). Define two new random variables through the transformations W=- Determine the joint pdf fz(, w) of the random variables Z and W in terms of the joint pdf ar (r,y) b) Assume that the random variables X and Y are jointly Gaussian, both are zero mean, both have the same variance ơ2 , and additionally are statistically independent. Use this information to obtain the joint...
Suppose the random variable X has PDF fX(x) = 3x2 when 0 < x < 1 and zero otherwise. What is the PDF of Y = 2X+3? a.Use the general method: Find the CDF of X and use it to get the PDF of Y b.Use a short-cut.
5. [20 points] X is a Gaussian random variable with zero mean and variance σ2. This random variable is passed through a hard-limiter device whose input-output relation is b r <0 Find the PDF of the output random variable Yg(X)
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...