explan the answer 7. Let X~ N(0, 1) and let Y xi. Find the probability density function of Y and, hence or otherwise, find the mean and variance of Y .
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find 2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
(1 point) Let f(x Scxºy? if 0 < x < 1, 0 SY51 otherwise Find the following: (a) c such that f(x,y) is a probability density function: c= (b) Expected values of X and Y: E(X) = E(Y) = 100 (c) Are X and Y independent? (enter YES or NO)
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a random variable following N(1.8). Assume X and Y are independent. Let W-min(x.Y). Find P(W 3) (b) (8 marks) The continuous random variables X and Y have the following joint probability density function: 4x 0, otherwise Find the joint probability density function of U and V where U-X+Y and -ky Also draw the support of the joint probability density function of Uand V (o (5...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0 otherwise. a. Find the probability P(X< Y). Give your answer to 4 decimal places. 28 Submit Answer Tries 0/5 b. Find the marginal probability density function of X, fx(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division and л for power. For...
explan the answer 10: A certain continuous distribution has cumulative distribution function (CDF) given by F(r) 0, <0 where θ is an unknown parameter, θ > 0. (i) Find (a) the p.d.f., (b) the mean and (e) the variance of this distribution. (ii) Suppose that X (Xi, X2, Xn) is a random sample from this distribu- tion and let Y max(Xi, XXn). Find the CDF and p.d.f. of Y. Hence find the value of a for which EloY)
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) ------------------------------------------------------------------------------------------------------------------------- Q2) The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean, and flat power spectral density, Let X(t) be a white Gaussian noise process that is input to...