A random process is generated as follows: X(t) = e−A|t|, where A is a random variable with pdf fA(a) = u(a) − u(a − 1) (1/seconds).
a) For a specific time, t, determine the pdf of X(t).
A random process is generated as follows: X(t) = e−A|t|, where A is a random variable...
A random process is generated as follows: X(t) = e−A|t|, where A is a random variable with pdf fA(a) = u(a) − u(a − 1) (1/seconds). a) Sketch several members of the ensemble. b) For a specific time, t, over what values of amplitude does the random variable X(t) range? c) For a specific time, t, find the mean and mean-squared value of X(t). d) For a specific time, t, determine the pdf of X(t).
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 +...
324. Consider the random process X(t) = A + Bt2 for - <t < oo, where A and B are two statistically independent Gaussian random variables, each with zero mean and variance o?. a) Plot two sample functions of X(t). b) Find E{X(0)} c) Find the autocorrelation function Rx(t,t +T). d) Find the pdf of the random variable Y = X(1). e) Is X(t) a Gaussian process? Prove your result.
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...
A random variable X has the following pdf, where is the parameter, f(x) = x>1. 2+1 Use the method of transformation to determine the pdf of Y = In X. Identify this distribution. X and Y are random variables with the following joint pdf, f(t,y) = e-(z+y), x >0, y>0. Find the joint probability density function of U and V by considering the transformation U x*y and V = Y. Hence, obtain the marginal density function of U
A stochastic process X() is defined by where A is a Gaussian-distributed random variable of zero mean and variance σ·The process Xt) is applied to an ideal integrator, producing the output YO)X(r) dr a. Determine the probability density function of the output Y) at a particular time t b. Determine whether or not Y) is strictly stationary Continuing with Problem 4.3, detemine whether or not the integrator output YC) produced in response to the input process Xit) is ergodic.
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Consider a random process X(t) defined by X(t) - Ycoset, 0st where o is a constant 1. and Y is a uniform random variable over (0,1) (a) Classify X(t) (b) Sketch a few (at least three) typical sample function of X(t) (c) Determine the pdfs of X(t) at t 0, /4o, /2, o. (d) EX() (e) Find the autocorrelation function Rx(t,s) of X(t) (f) Find the autocovariance function Rx(t,s) of X(t)
Consider a random process X(t) defined by X(t) -...
2. Consider the random process x(t) defined by x(t) a cos(wt 6), where w and 0 are constants, and a is a random variable uniformly distributed in the range (-A, A). a. Sketch the ensemble (sample functions) representing x(t). (2.5 points). b. Find the mean and variance of the random variable a. (5 points). c. Find the mean of x(t), m(t) E((t)). (5 points). d. Find the autocorrelation of x(t), Ra (t1, t2) E(x (t)x2 )). (5 points). Is the...
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)....
Assume the continuous random variable X follows the uniform
[0,1] distribution, and define another random variable
We were unable to transcribe this imagea) Determine the CDF of Y. Hint: start by writing P(Y ), then show that P(Y y) = P(X s g(v)), where g(y) is a function that you need to determine. b) Determine the PDF of Y.