q. If X is Rayleigh distributed amplitude with an average power of 10, what is the pdf of Y=1-exp(-X^2/10)?
r. If X is N(0,4) and Y is N(0,9) and X and Y are independent, what is the prob {XY>0)?
q. If X is Rayleigh distributed amplitude with an average power of 10, what is the...
If X is Rayleigh distributed amplitude with an average power of 10, what is the pdf of Y-1-exp(-XA2/10)? If X is N(0,4) and Y is N(0,9) and X and Y are independent, what is the prob (XY>0)?
Problem 5: Noisy Signal A signal generator generates a random sinusoid, X cos (2nt + Θ) whose amplitude is given by a random variable X uniformly distributed between-1 and 1, and phase Θ is an independent random variable which takes each of the following values π 0, π with equal prob- ability. This signal's amplitude is additively corrupted by independent noise YN(0, 0.01) The output amplitude is denoted by Z, where Z-X +Y. Assuming that an estimator of X has...
5. Random variables X U[0, 1 and Y ~Exp(1) are independent (a) Compute P(X Y > z) for the case 0 S1 and the case z >1. b) Compute and plot the pdf of XY. (c) Give the MGF of X Y.
5. Random variables X U[0, 1 and Y ~Exp(1) are independent (a) Compute P(X Y > z) for the case 0 S1 and the case z >1. b) Compute and plot the pdf of XY. (c) Give the...
5. If X and Y are independent and identically distributed with Exponential(A), compute El and 6. Let R be the region bounded by the points (0, 1), (-1,0) and (1,0). Joint pdf of (x, Y) is: 1, if (r,y) e R 0, otherwise. Compute P(X-1, γ 7. If X U(0,1) and Y U(0, 1) independent random variables, find the joint pdf of (X+y,x -Y). Also compute marginal pdf of X+Y 8. If x Ezpomential(0.5) and Y ~ Erponential0.5) independent random...
X is exponentially distributed density of the power expressed in mW with an average of 5 mw Obtain the pdf of the power expressed in dBm units.
In response to comment 'na' what exactly are you saying?
Question 4 [16 marks] X Y (a) The random vector has probability density function fx.y (x, y)exp {-22 - 2xy - 3y*}, where k is some constant. (i) Find k N (0, 3/2) and Y ~ N (0,1/2) 11 Show that X Find cov (X, Y) and corr (X, Y) 111 (iv) Find E (Y|X) (b) The random variables U and V are distributed with mean 1/A, while V is...
Let X and Y be independent uniform distributed random variables, 0 < X < 1 and 1 < Y < 2. Let Z = X + Y. What is the pdf of Z?
Question 3 [17 marks] The random variable X is distributed exponentially with parameter A i.e. X~ Exp(A), so that its probability density function (pdf) of X is SO e /A fx(x) | 0, (2) (a) Let Y log(X. When A = 1, (i) Show that the pdf of Y is fr(y) = e (u+e-") (ii) Derive the moment generating function of Y, My(t), and give the values of t such that My(t) is well defined. (b) Suppose that Xi, i...
The random variables X1, X2, - .. are independent and identically distributed with common pdf 0 х > fx (x;0) (2) ; х<0. This distribution has many applications in engineering, and is known as the Rayleigh distribution. 2 (a) Show that if X has pdf given by (2), then Y = X2/0 is x2, i.e. T (1, 2) i.e. exponential with mean 2, with pdf fr (y;0) - ; y0; (b) Show that the maximum likelihood estimator of 0 is...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0