[CLU: Let g(t) be the rectangular pulse shown in Fig. Q3. The random process X(t) is...
Let X(t) and Y(t) be independent, wide-sense stationary random process with zero means and the same covariance function Cx(t) Let Z(t) be defined by Z(t) = X(t)coswt + Y(t)sinwt Find the joint pdf of X(t1) and X(t2) in part b
Fig.1 (a) shows a staircase like signal x(t) and Fig.1 (b) shows the rectangular pulse g(t) Express x(t) in terms of g(t). xit) 4 2 g(t) -1 0 1 Fig.1
A Random Telegraph Signal with rate λ > 0 is a random process X(t) (where for each t, X(t) ∈ {±1}) defined on [0,∞) with the following properties: X(0) = ±1 with probability 0.5 each, and X(t) switches between the two values ±1 at the points of arrival of a Poisson process with rate λ i.e., the probability of k changes in a time interval of length T isP(k sign changes in an interval of length T) = e −λT...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...
Consider a random process where rectangular pulses of width 1 are separated in time by intervals of T seconds The amplitude of each pulse is determined independently and with equal probability to be either 1 0, or -1.Pulses begin at periodic time instants to t nT where to is a random variable that is uniformly distributed over the range O to T. Asample function is shown below. to -T to+ T to +37 to to + 27 to + 4T...
nice handwriting please. Question 2 (30 Points) Consider a random process where rectangular pulses of width T, are separated in time by intervals of T seconds. The amplitude of each pulse is determined independently and with equal probability to be either 1, 0, or -1. Pulses begin at periodic time instants to tnt where to is a random variable that is uniformly distributed over the range 0 to T. A sample function is shown below. X(t). T; to-T to +...
Problem 4 Let X and y be independent Poisson(A) and Poisson(A2) random variables, respectively. i. Write an expression for the PMF of Z -X + Y. i.e.. pz[n] for all possible n. ii. Write an expression for the conditional PMF of X given that Z-n, i.e.. pxjz[kn for all possible k. Which random variable has the same PMF, i.e., is this PMF that of a Bernoulli, binomial, Poisson, geometric, or uniform random variable (which assumes all possible values with equal...
Problem 1 (4 points) Let h(t) be the triangular pulse shown in the Figure and let x(t) be the impulse train given with h(t) -1 2T-T T 27 Determine and sketch y(t)- x(t) * h(t) for the following values of T ·T=2 3 2
2. Consider the random process x(t) defined by x(t) a cos(wt + 6).where w and a are constants, and 0 is a random variable uniformly distributed in the range (-T, ) Sketch the ensemble (sample functions) representing x(t). (2.5 points). a. b. Find the mean and variance of the random variable 0. (2.5 points). Find the mean of x(t), m (t) E(x(t)). (2.5 points). c. d. Find the autocorrelation of x(t), R (t,, t) = E(x, (t)x2 (t)). (5 points)....